Extension: [46,7,9] to [51,8,9] Number of the matrices for extension:18 Weights: 9 18 27 36 45 Maximal number for proportional coordinatesTill dimension 1--51; Till dimension 2--51; Till dimension 3--51; Till dimension 4--51; Till dimension 5--51; Till dimension 6--51; Till dimension 7--51; Till dimension 8--51; The minimum distace of the dual codes is: 2 ============================================ Start matrix 1 8 51 1 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 222111002221110002221112220022200220000000000010000 222111002221112220002221110022200002200000000001000 222111002222221112220001110022200000022000000000100 210210212100000000000000000000000000000000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 8888881_8 1 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 222111002221110002221112220022200220000000000010000 222111002221112220002221110022200002200000000001000 222111002222221112220001110022200000022000000000100 210210212100000000000000000000000000000000000000010 000000000001201201201201201212012121212111100000001 AUT: 10077696 $1z^{0}+8z^{9}+42z^{18}+1346z^{27}+5164z^{36} dd-2$\\ Start matrix 1 8 51 2 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 222111002222221112220001110022200220000000000010000 111222001111112220002221110022200002200000000001000 111222001111110002221112220022200000022000000000100 210210212100000000000000000000000000000000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 8888882_8 2 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 222111002222221112220001110022200220000000000010000 111222001111112220002221110022200002200000000001000 111222001111110002221112220022200000022000000000100 210210212100000000000000000000000000000000000000010 000000000012001201201201201212012121212111100000001 AUT: 100776960 $1z^{0}+8z^{9}+60z^{18}+1310z^{27}+5182z^{36} dd-2$\\ Start matrix 1 8 51 3 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 111222002222221112222221110000000220000000000010000 111222001111111112222220000022200002200000000001000 222111002221112220000000000000000000022000000000100 210210210000002100000000000000000000000000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 8888883_8 3 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 111222002222221112222221110000000220000000000010000 111222001111111112222220000022200002200000000001000 222111002221112220000000000000000000022000000000100 210210210000002100000000000000000000000000000000010 000000001201200001122001201212012121212111100000001 AUT: 3359232 $1z^{0}+10z^{9}+90z^{18}+1244z^{27}+5216z^{36} dd-2$\\ Start matrix 1 8 51 4 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 111222002222221112222221110000000220000000000010000 111222001111111112222220000022200002200000000001000 210210210000002100000000000000000000000000000000100 000000002221110000000000000000000000022000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 8888884_8 4 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 111222002222221112222221110000000220000000000010000 111222001111111112222220000022200002200000000001000 210210210000002100000000000000000000000000000000100 000000002221110000000000000000000000022000000000010 000000001201200001122001201212012121212111100000001 AUT: 10077696 $1z^{0}+12z^{9}+84z^{18}+1250z^{27}+5214z^{36} dd-2$\\ Start matrix 1 8 51 5 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 111222002222221112222221110000000220000000000010000 222111001111112222222220000022200002200000000001000 222111002221112220000000000000000000022000000000100 210210210000002100000000000000000000000000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 8888885_8 5 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 111222002222221112222221110000000220000000000010000 222111001111112222222220000022200002200000000001000 222111002221112220000000000000000000022000000000100 210210210000002100000000000000000000000000000000010 000000001201200001122001201212012121212111100000001 AUT: 5038848 $1z^{0}+8z^{9}+96z^{18}+1238z^{27}+5218z^{36} dd-2$\\ Start matrix 1 8 51 6 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 222111002222222222222221110000000220000000000010000 111222001111111112222220000022200002200000000001000 222111002222221110000000000000000000022000000000100 210210212100000000000000000000000000000000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 8888886_8 6 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 222111002222222222222221110000000220000000000010000 111222001111111112222220000022200002200000000001000 222111002222221110000000000000000000022000000000100 210210212100000000000000000000000000000000000000010 000000000012001201122001201212012121212111100000001 AUT: 20155392 $1z^{0}+12z^{9}+102z^{18}+1214z^{27}+5232z^{36} dd-2$\\ Start matrix 1 8 51 7 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 222111002222222222222221110000000220000000000010000 111222001111111112222220000022200002200000000001000 210210212100000000000000000000000000000000000000100 000000000022211100000000000000000000022000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 8888887_8 7 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 222111002222222222222221110000000220000000000010000 111222001111111112222220000022200002200000000001000 210210212100000000000000000000000000000000000000100 000000000022211100000000000000000000022000000000010 000000000012012001122001201212012121212111100000001 AUT: 60466176 $1z^{0}+14z^{9}+78z^{18}+1256z^{27}+5212z^{36} dd-2$\\ Start matrix 1 8 51 8 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 222111002222222222222221110000000220000000000010000 111222001111111112222220000022200002200000000001000 210210212100000000000000000000000000000000000000100 000000000000000002221110000000000000022000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 8888888_8 8 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 222111002222222221111110000022222000000000000100000 222111002222222222222221110000000220000000000010000 111222001111111112222220000022200002200000000001000 210210212100000000000000000000000000000000000000100 000000000000000002221110000000000000022000000000010 000000000011220001201201201212012121212111100000001 AUT: 181398528 $1z^{0}+14z^{9}+114z^{18}+1184z^{27}+5248z^{36} dd-2$\\ Start matrix 1 8 51 9 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 222111002222102102121000000000000000000000000010000 222111002220000000000222222220000000000000000001000 222111002220000000000222111002200000000000000000100 000000000000000000000000000000022222222000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 8888889_8 9 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 222111002222102102121000000000000000000000000010000 222111002220000000000222222220000000000000000001000 222111002220000000000222111002200000000000000000100 000000000000000000000000000000022222222000000000010 120120121200000000000120120121211122200111100000001 AUT: 20155392 $1z^{0}+14z^{9}+186z^{18}+1040z^{27}+5320z^{36} dd-2$\\ Start matrix 1 8 51 10 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 222111002222102102121000000000000000000000000010000 222111002220000000000222222220000000000000000001000 222111002220000000000222111002200000000000000000100 222111002220000000000000000000022222222000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 88888810_8 10 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 222111002222102102121000000000000000000000000010000 222111002220000000000222222220000000000000000001000 222111002220000000000222111002200000000000000000100 222111002220000000000000000000022222222000000000010 120120121200000000000120120121211122200111100000001 AUT: 10077696 $1z^{0}+12z^{9}+192z^{18}+1034z^{27}+5322z^{36} dd-2$\\ Start matrix 1 8 51 11 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 222111002222102102121000000000000000000000000010000 222111002220000000000222222220000000000000000001000 000000000000000000000000000002222222200000000000100 000000000000000000000000000002221110022000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 88888811_8 11 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 222111002222102102121000000000000000000000000010000 222111002220000000000222222220000000000000000001000 000000000000000000000000000002222222200000000000100 000000000000000000000000000002221110022000000000010 120120121200000000000111222001201201212111100000001 AUT: 40310784 $1z^{0}+18z^{9}+174z^{18}+1052z^{27}+5316z^{36} dd-2$\\ Start matrix 1 8 51 12 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 222111002222102102121000000000000000000000000010000 000000000000000000000222222220000000000000000001000 000000000000000000000222111002200000000000000000100 000000000000000000000000000000022222222000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 88888812_8 12 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 222111002222102102121000000000000000000000000010000 000000000000000000000222222220000000000000000001000 000000000000000000000222111002200000000000000000100 000000000000000000000000000000022222222000000000010 120120121200000000000120120121211122200111100000001 AUT: 80621568 $1z^{0}+20z^{9}+186z^{18}+1022z^{27}+5332z^{36} dd-2$\\ Start matrix 1 8 51 13 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 222111002220000000000222222220000000000000000010000 000000000000000000000000000002222222200000000001000 000000000000000000000000000002221110022000000000100 000000000000000000000000000002102102121000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 88888813_8 13 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 222111002220000000000222222220000000000000000010000 000000000000000000000000000002222222200000000001000 000000000000000000000000000002221110022000000000100 000000000000000000000000000002102102121000000000010 120120121201201201212111222000000000000111100000001 AUT: 262020096 $1z^{0}+30z^{9}+138z^{18}+1088z^{27}+5304z^{36} dd-2$\\ Start matrix 1 8 51 14 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 000000000000000000000222222220000000000000000010000 000000000000000000000222111002200000000000000001000 000000000000000000000210210212100000000000000000100 000000000000000000000000000000022222222000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 88888814_8 14 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002222221110022000000000000000000000000100000 000000000000000000000222222220000000000000000010000 000000000000000000000222111002200000000000000001000 000000000000000000000210210212100000000000000000100 000000000000000000000000000000022222222000000000010 120120121122001201212000000000011122200111100000001 AUT: 524040192 $1z^{0}+32z^{9}+186z^{18}+986z^{27}+5356z^{36} dd-2$\\ Start matrix 1 8 51 15 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 210210212222222222100000000000000000000000000100000 000000000000000000022222222000000000000000000010000 000000000000000000022211100220000000000000000001000 000000000000000000000000000002222222200000000000100 000000000000000000000000000002221110022000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 88888815_8 15 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 210210212222222222100000000000000000000000000100000 000000000000000000022222222000000000000000000010000 000000000000000000022211100220000000000000000001000 000000000000000000000000000002222222200000000000100 000000000000000000000000000002221110022000000000010 000000001112220000012012012121201201212111100000001 AUT: 644972544 $1z^{0}+24z^{9}+210z^{18}+962z^{27}+5364z^{36} dd-2$\\ Start matrix 1 8 51 16 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002220000000022222222000000000000000000100000 111222000002222220011100000220000000000000000010000 000000000000000000000000000002222222200000000001000 000000000000000000000000000002221110022000000000100 000000000000000000000000000002102102121000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 88888816_8 16 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 222111002220000000022222222000000000000000000100000 111222000002222220011100000220000000000000000010000 000000000000000000000000000002222222200000000001000 000000000000000000000000000002221110022000000000100 000000000000000000000000000002102102121000000000010 120120121201122001212011220120000000000111100000001 AUT: 174680064 $1z^{0}+28z^{9}+90z^{18}+1190z^{27}+5252z^{36} dd-2$\\ Start matrix 1 8 51 17 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 000000000000000000022222222000000000000000000100000 000000000000000000022211100220000000000000000010000 000000000000000000021021021210000000000000000001000 000000000000000000000000000002222222200000000000100 000000000000000000000000000002221110022000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 88888817_8 17 111111110000000000000000000000000000000000010000000 222111002222222222200000000000000000000000001000000 000000000000000000022222222000000000000000000100000 000000000000000000022211100220000000000000000010000 000000000000000000021021021210000000000000000001000 000000000000000000000000000002222222200000000000100 000000000000000000000000000002221110022000000000010 120120121111222200000000000001201201212111100000001 AUT: 1048080384 $1z^{0}+36z^{9}+282z^{18}+782z^{27}+5460z^{36} dd-2$\\ Start matrix 1 8 51 18 111111110000000000000000000000000000000000010000000 000000002222222222222222200000000000000000001000000 000000002222221111110000022222000000000000000100000 000000002221112221110000000000222220000000000010000 000000000002222222220000022200222002200000000001000 222111000000000000000000000000000000022000000000100 210210210000000000000000000000000000021000000000010 000000000000000000000000000000000000000111100000001 ?8 51 3 88888818_8 18 111111110000000000000000000000000000000000010000000 000000002222222222222222200000000000000000001000000 000000002222221111110000022222000000000000000100000 000000002221112221110000000000222220000000000010000 000000000002222222220000022200222002200000000001000 222111000000000000000000000000000000022000000000100 210210210000000000000000000000000000021000000000010 000000001201201201201122012012120121200111100000001 AUT: 262020096 $1z^{0}+26z^{9}+42z^{18}+1292z^{27}+5200z^{36} dd-2$\\ DIFFERENT ENUMERATORS :18 ALL CODES: 18 1 1 AUT: 10077696 $1z^{0}+8z^{9}+42z^{18}+1346z^{27}+5164z^{36} dd-2$\\ 2 1 AUT: 100776960 $1z^{0}+8z^{9}+60z^{18}+1310z^{27}+5182z^{36} dd-2$\\ 3 1 AUT: 3359232 $1z^{0}+10z^{9}+90z^{18}+1244z^{27}+5216z^{36} dd-2$\\ 4 1 AUT: 10077696 $1z^{0}+12z^{9}+84z^{18}+1250z^{27}+5214z^{36} dd-2$\\ 5 1 AUT: 5038848 $1z^{0}+8z^{9}+96z^{18}+1238z^{27}+5218z^{36} dd-2$\\ 6 1 AUT: 20155392 $1z^{0}+12z^{9}+102z^{18}+1214z^{27}+5232z^{36} dd-2$\\ 7 1 AUT: 60466176 $1z^{0}+14z^{9}+78z^{18}+1256z^{27}+5212z^{36} dd-2$\\ 8 1 AUT: 181398528 $1z^{0}+14z^{9}+114z^{18}+1184z^{27}+5248z^{36} dd-2$\\ 9 1 AUT: 20155392 $1z^{0}+14z^{9}+186z^{18}+1040z^{27}+5320z^{36} dd-2$\\ 10 1 AUT: 10077696 $1z^{0}+12z^{9}+192z^{18}+1034z^{27}+5322z^{36} dd-2$\\ 11 1 AUT: 40310784 $1z^{0}+18z^{9}+174z^{18}+1052z^{27}+5316z^{36} dd-2$\\ 12 1 AUT: 80621568 $1z^{0}+20z^{9}+186z^{18}+1022z^{27}+5332z^{36} dd-2$\\ 13 1 AUT: 262020096 $1z^{0}+30z^{9}+138z^{18}+1088z^{27}+5304z^{36} dd-2$\\ 14 1 AUT: 524040192 $1z^{0}+32z^{9}+186z^{18}+986z^{27}+5356z^{36} dd-2$\\ 15 1 AUT: 644972544 $1z^{0}+24z^{9}+210z^{18}+962z^{27}+5364z^{36} dd-2$\\ 16 1 AUT: 174680064 $1z^{0}+28z^{9}+90z^{18}+1190z^{27}+5252z^{36} dd-2$\\ 17 1 AUT: 1048080384 $1z^{0}+36z^{9}+282z^{18}+782z^{27}+5460z^{36} dd-2$\\ 18 1 AUT: 262020096 $1z^{0}+26z^{9}+42z^{18}+1292z^{27}+5200z^{36} dd-2$\\ Extension: [47,7,9] to [51,8,9] Number of the matrices for extension:36 Weights: 9 18 27 36 45 Maximal number for proportional coordinatesTill dimension 1--51; Till dimension 2--51; Till dimension 3--51; Till dimension 4--51; Till dimension 5--51; Till dimension 6--51; Till dimension 7--51; Till dimension 8--51; The minimum distace of the dual codes is: 2 ============================================ Start matrix 1 8 51 1 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220222222222022222222000000000010000 000000001111111110222222222022211100220000000001000 000000002222222220222222222021021021210000000000100 000000002221110000000000000000000000002200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 8888881_8 1 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220222222222022222222000000000010000 000000001111111110222222222022211100220000000001000 000000002222222220222222222021021021210000000000100 000000002221110000000000000000000000002200000000010 000000001201201200111222000000000000001211100000001 AUT: 93312 $1z^{0}+6z^{9}+138z^{18}+1160z^{27}+5256z^{36} dd-2$\\ Start matrix 1 8 51 2 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220222222222022222222000000000010000 000000001111111110222222222022211100220000000001000 000000002222222220222222222021021021210000000000100 000000002221110000222222222000000000002200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 8888882_8 2 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220222222222022222222000000000010000 000000001111111110222222222022211100220000000001000 000000002222222220222222222021021021210000000000100 000000002221110000222222222000000000002200000000010 000000001201201200111222000000000000001211100000001 AUT: 46656 $1z^{0}+4z^{9}+144z^{18}+1154z^{27}+5258z^{36} dd-2$\\ Start matrix 1 8 51 3 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220222222222022222222000000000010000 000000001111111110222222222022211100220000000001000 000000002221110000000000000000000000002200000000100 000000002102102100000000000000000000002100000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 8888883_8 3 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220222222222022222222000000000010000 000000001111111110222222222022211100220000000001000 000000002221110000000000000000000000002200000000100 000000002102102100000000000000000000002100000000010 000000000000000000111222000012012012120011100000001 AUT: 186624 $1z^{0}+10z^{9}+126z^{18}+1172z^{27}+5252z^{36} dd-2$\\ Start matrix 1 8 51 4 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220222222222022222222000000000010000 000000002222222220222222222022211100220000000001000 000000002222222220222222222021021021210000000000100 000000002221110000000000000000000000002200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 8888884_8 4 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220222222222022222222000000000010000 000000002222222220222222222022211100220000000001000 000000002222222220222222222021021021210000000000100 000000002221110000000000000000000000002200000000010 000000001201201200111222000000000000001211100000001 AUT: 559872 $1z^{0}+12z^{9}+120z^{18}+1178z^{27}+5250z^{36} dd-2$\\ Start matrix 1 8 51 5 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000002102102100222222222021000000000000000001000 000000002222222220222111000000220000000000000000100 000000000000000000000000000000002222222200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 8888885_8 5 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000002102102100222222222021000000000000000001000 000000002222222220222111000000220000000000000000100 000000000000000000000000000000002222222200000000010 000000000000000000120120120000121112220011100000001 AUT: 373248 $1z^{0}+6z^{9}+138z^{18}+1160z^{27}+5256z^{36} dd-2$\\ Start matrix 1 8 51 6 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000002102102100222222222021000000000000000001000 000000000000000000222222222000222222220000000000100 000000000000000000000000000000222111002200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 8888886_8 6 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000002102102100222222222021000000000000000001000 000000000000000000222222222000222222220000000000100 000000000000000000000000000000222111002200000000010 000000000000000000111222000000120120121211100000001 AUT: 839808 $1z^{0}+6z^{9}+156z^{18}+1124z^{27}+5274z^{36} dd-2$\\ ?8 51 3 8888886_8 7 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000002102102100222222222021000000000000000001000 000000000000000000222222222000222222220000000000100 000000000000000000000000000000222111002200000000010 000000002222222220111222000000120120121211100000001 AUT: 419904 $1z^{0}+6z^{9}+138z^{18}+1160z^{27}+5256z^{36} dd-2$\\ Start matrix 1 8 51 7 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000002102102100222222222021000000000000000001000 000000000000000000222111000000220000000000000000100 000000000000000000000000000000002222222200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 8888887_8 8 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000002102102100222222222021000000000000000001000 000000000000000000222111000000220000000000000000100 000000000000000000000000000000002222222200000000010 000000000000000000120120120000121112220011100000001 AUT: 1679616 $1z^{0}+8z^{9}+150z^{18}+1130z^{27}+5272z^{36} dd-2$\\ ?8 51 3 8888887_8 9 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000002102102100222222222021000000000000000001000 000000000000000000222111000000220000000000000000100 000000000000000000000000000000002222222200000000010 000000002222222220120120120000121112220011100000001 AUT: 839808 $1z^{0}+8z^{9}+132z^{18}+1166z^{27}+5254z^{36} dd-2$\\ Start matrix 1 8 51 8 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000002102102100222222222021000000000000000001000 000000000000000000000000000000222222220000000000100 000000000000000000000000000000222111002200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 8888888_8 10 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000002102102100222222222021000000000000000001000 000000000000000000000000000000222222220000000000100 000000000000000000000000000000222111002200000000010 000000000000000000111222000000120120121211100000001 AUT: 6718464 $1z^{0}+12z^{9}+138z^{18}+1142z^{27}+5268z^{36} dd-2$\\ ?8 51 3 8888888_8 11 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000002102102100222222222021000000000000000001000 000000000000000000000000000000222222220000000000100 000000000000000000000000000000222111002200000000010 000000002222222220111222000000120120121211100000001 AUT: 3359232 $1z^{0}+12z^{9}+120z^{18}+1178z^{27}+5250z^{36} dd-2$\\ Start matrix 1 8 51 9 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000000000000000222222222000222222220000000001000 000000000000000000222222222000222111002200000000100 000000000000000000000000000000210210212100000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 8888889_8 12 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000000000000000222222222000222222220000000001000 000000000000000000222222222000222111002200000000100 000000000000000000000000000000210210212100000000010 000000001201201200111222000012000000000011100000001 AUT: 559872 $1z^{0}+10z^{9}+144z^{18}+1136z^{27}+5270z^{36} dd-2$\\ Start matrix 1 8 51 10 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000000000000000222111000000220000000000000001000 000000000000000000210210210000210000000000000000100 000000000000000000000000000000002222222200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888810_8 13 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000000000000000222111000000220000000000000001000 000000000000000000210210210000210000000000000000100 000000000000000000000000000000002222222200000000010 000000001201201200000000000012001112220011100000001 AUT: 1119744 $1z^{0}+12z^{9}+138z^{18}+1142z^{27}+5268z^{36} dd-2$\\ Start matrix 1 8 51 11 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000000000000000000000000000222222220000000001000 000000000000000000000000000000222111002200000000100 000000000000000000000000000000210210212100000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888811_8 14 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000222222222022000000000000000010000 000000000000000000000000000000222222220000000001000 000000000000000000000000000000222111002200000000100 000000000000000000000000000000210210212100000000010 000000001201201200111222000012000000000011100000001 AUT: 14556672 $1z^{0}+28z^{9}+90z^{18}+1190z^{27}+5252z^{36} dd-2$\\ Start matrix 1 8 51 12 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220000000000022222222000000000010000 000000002222222220000000000022211100220000000001000 000000002222222220000000000021021021210000000000100 000000002221110000000000000000000000002200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888812_8 15 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220000000000022222222000000000010000 000000002222222220000000000022211100220000000001000 000000002222222220000000000021021021210000000000100 000000002221110000000000000000000000002200000000010 000000001201201200111222000000000000001211100000001 AUT: 2239488 $1z^{0}+12z^{9}+174z^{18}+1070z^{27}+5304z^{36} dd-2$\\ Start matrix 1 8 51 13 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220000000000022222222000000000010000 000000002222222220000000000022211100220000000001000 000000002222222220000000000021021021210000000000100 000000000000000000222111000000000000002200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888813_8 16 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220000000000022222222000000000010000 000000002222222220000000000022211100220000000001000 000000002222222220000000000021021021210000000000100 000000000000000000222111000000000000002200000000010 000000001112220000120120120000000000001211100000001 AUT: 1119744 $1z^{0}+12z^{9}+138z^{18}+1142z^{27}+5268z^{36} dd-2$\\ Start matrix 1 8 51 14 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220000000000022222222000000000010000 000000002222222220000000000022211100220000000001000 000000000000000000222111000000000000002200000000100 000000000000000000210210210000000000002100000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888814_8 17 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220000000000022222222000000000010000 000000002222222220000000000022211100220000000001000 000000000000000000222111000000000000002200000000100 000000000000000000210210210000000000002100000000010 000000001112220000000000000012012012120011100000001 AUT: 3359232 $1z^{0}+12z^{9}+138z^{18}+1142z^{27}+5268z^{36} dd-2$\\ ?8 51 3 88888814_8 18 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002222222220000000000022222222000000000010000 000000002222222220000000000022211100220000000001000 000000000000000000222111000000000000002200000000100 000000000000000000210210210000000000002100000000010 000000001112220000222222222012012012120011100000001 AUT: 1679616 $1z^{0}+12z^{9}+120z^{18}+1178z^{27}+5250z^{36} dd-2$\\ Start matrix 1 8 51 15 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000000000000022000000000000000010000 000000002102102100000000000021000000000000000001000 000000000000000000222111000000220000000000000000100 000000000000000000000000000000002222222200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888815_8 19 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000000000000022000000000000000010000 000000002102102100000000000021000000000000000001000 000000000000000000222111000000220000000000000000100 000000000000000000000000000000002222222200000000010 000000000000000000120120120000121112220011100000001 AUT: 6718464 $1z^{0}+14z^{9}+150z^{18}+1112z^{27}+5284z^{36} dd-2$\\ ?8 51 3 88888815_8 20 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000000000000022000000000000000010000 000000002102102100000000000021000000000000000001000 000000000000000000222111000000220000000000000000100 000000000000000000000000000000002222222200000000010 000000002222222220120120120000121112220011100000001 AUT: 3359232 $1z^{0}+14z^{9}+132z^{18}+1148z^{27}+5266z^{36} dd-2$\\ Start matrix 1 8 51 16 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000000000000022000000000000000010000 000000002102102100000000000021000000000000000001000 000000000000000000000000000000222222220000000000100 000000000000000000000000000000222111002200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888816_8 21 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000000000000022000000000000000010000 000000002102102100000000000021000000000000000001000 000000000000000000000000000000222222220000000000100 000000000000000000000000000000222111002200000000010 000000000000000000111222000000120120121211100000001 AUT: 26873856 $1z^{0}+18z^{9}+174z^{18}+1052z^{27}+5316z^{36} dd-2$\\ ?8 51 3 88888816_8 22 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000000000000022000000000000000010000 000000002102102100000000000021000000000000000001000 000000000000000000000000000000222222220000000000100 000000000000000000000000000000222111002200000000010 000000002222222220111222000000120120121211100000001 AUT: 13436928 $1z^{0}+18z^{9}+156z^{18}+1088z^{27}+5298z^{36} dd-2$\\ Start matrix 1 8 51 17 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000000000000022000000000000000010000 000000000000000000000000000000222222220000000001000 000000000000000000000000000000222111002200000000100 000000000000000000000000000000210210212100000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888817_8 23 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222111111111100000000000000000100000 000000002221110000000000000022000000000000000010000 000000000000000000000000000000222222220000000001000 000000000000000000000000000000222111002200000000100 000000000000000000000000000000210210212100000000010 000000001201201200111222000012000000000011100000001 AUT: 58226688 $1z^{0}+30z^{9}+138z^{18}+1088z^{27}+5304z^{36} dd-2$\\ Start matrix 1 8 51 18 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 111222002222222222221111110022000000000000000100000 222111002222222220002220000000222222220000000010000 222111002222222220002220000000222111002200000001000 222111002222222220002220000000210210212100000000100 210210210000000000002100000000000000000000000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888818_8 24 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 111222002222222222221111110022000000000000000100000 222111002222222220002220000000222222220000000010000 222111002222222220002220000000222111002200000001000 222111002222222220002220000000210210212100000000100 210210210000000000002100000000000000000000000000010 000000001112220001200001201212000000000011100000001 AUT: 4478976 $1z^{0}+16z^{9}+108z^{18}+1190z^{27}+5246z^{36} dd-2$\\ Start matrix 1 8 51 19 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 111222002222222222221111110022000000000000000100000 222111000000000000002220000000222222220000000010000 222111000000000000002220000000222111002200000001000 222111000000000000002220000000210210212100000000100 210210210000000000002100000000000000000000000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888819_8 25 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 111222002222222222221111110022000000000000000100000 222111000000000000002220000000222222220000000010000 222111000000000000002220000000222111002200000001000 222111000000000000002220000000210210212100000000100 210210210000000000002100000000000000000000000000010 000000001111222200000001201212000000000011100000001 AUT: 35831808 $1z^{0}+16z^{9}+270z^{18}+866z^{27}+5408z^{36} dd-2$\\ Start matrix 1 8 51 20 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 111222002222222222221111110022000000000000000100000 222111000000000000002220000000222222220000000010000 210210210000000000002100000000000000000000000001000 000000002221110000000000000000000000002200000000100 000000002102102100000000000000000000002100000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888820_8 26 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 111222002222222222221111110022000000000000000100000 222111000000000000002220000000222222220000000010000 210210210000000000002100000000000000000000000001000 000000002221110000000000000000000000002200000000100 000000002102102100000000000000000000002100000000010 000000000000000012000001201212111222000011100000001 AUT: 4478976 $1z^{0}+16z^{9}+126z^{18}+1154z^{27}+5264z^{36} dd-2$\\ Start matrix 1 8 51 21 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 111222002222222222221111110022000000000000000100000 210210210000000000002100000000000000000000000010000 000000002221110000000000000000220000000000000001000 000000002102102100000000000000210000000000000000100 000000000000000000000000000000002222222200000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888821_8 27 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 111222002222222222221111110022000000000000000100000 210210210000000000002100000000000000000000000010000 000000002221110000000000000000220000000000000001000 000000002102102100000000000000210000000000000000100 000000000000000000000000000000002222222200000000010 000000000000000012000012001212001112220011100000001 AUT: 17915904 $1z^{0}+18z^{9}+138z^{18}+1124z^{27}+5280z^{36} dd-2$\\ Start matrix 1 8 51 22 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 111222002222222222221111110022000000000000000100000 210210210000000000002100000000000000000000000010000 000000000000000000000000000000222222220000000001000 000000000000000000000000000000222111002200000000100 000000000000000000000000000000210210212100000000010 000000000000000000000000000000000000000011100000001 ?8 51 3 88888822_8 28 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 111222002222222222221111110022000000000000000100000 210210210000000000002100000000000000000000000010000 000000000000000000000000000000222222220000000001000 000000000000000000000000000000222111002200000000100 000000000000000000000000000000210210212100000000010 000000001111222200000012001212000000000011100000001 AUT: 465813504 $1z^{0}+34z^{9}+234z^{18}+884z^{27}+5408z^{36} dd-2$\\ Start matrix 1 8 51 23 111111110000000000000000000000000000000000010000000 222111002222222222222222222200000000000000001000000 210210212222222222222111100022200000000000000100000 201012122222222222210210021121100000000000000010000 012201122211000000000002201102220000000000000001000 012201121020210000000002201102210000000000000000100 000000000000000000000000000000002222222200000000010 000000000000000000000000000000000000000011100000001 Extension: [49,7,9] to [51,8,9] Number of the matrices for extension:209 Weights: 9 18 27 36 45 Maximal number for proportional coordinatesTill dimension 1--51; Till dimension 2--51; Till dimension 3--51; Till dimension 4--51; Till dimension 5--51; Till dimension 6--51; Till dimension 7--51; Till dimension 8--51; The minimum distace of the dual codes is: 2 ============================================ Start matrix 1 8 51 1 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 111222002222222222110222222222211021121000000010000 210210212222222222102111111111120102122100000001000 000000002221110000000222222222000000000022000000100 000000002102102100000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 2 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 111222002222222222110222222222211021121000000010000 210210212222222222102111111111120102122100000001000 000000002221110000000000000000000000000022000000100 000000002102102100000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 3 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 111222002222222222110222222222211021121000000010000 210210212111111111102222222222120102122100000001000 000000000222111000000222222222000000000022000000100 000000000210210210000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 4 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 111222002222222222110222222222211021121000000010000 210210212111111111102222222222120102122100000001000 000000000222111000000000000000000000000022000000100 000000000210210210000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 5 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 111222002222222222110222222222211021121000000010000 210210212222222222102222222222120102122100000001000 000000002221110000000222222222000000000022000000100 000000002102102100000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 6 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 111222002222222222110222222222211021121000000010000 210210212222222222102222222222120102122100000001000 000000000000000000000222111000000000000022000000100 000000000000000000000210210210000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 7 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 111222002222222222110222222222211021121000000010000 210210212222222222102222222222120102122100000001000 000000002221110000000000000000000000000022000000100 000000002102102100000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 8 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 111222002222222222110222222222211021121000000010000 210210212000000000102222222222120102122100000001000 000000000222222222000222111000000000000022000000100 000000000000000000000210210210000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 9 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 111222002222222222110222222222211021121000000010000 210210212000000000102222222222120102122100000001000 000000000000000000000222111000000000000022000000100 000000000000000000000210210210000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 10 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 210210212222210211200211111111122122220022000001000 201012122221022221220222222222221122022020000000100 201012122102222212202200000000012120220202000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 11 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 210210212222210211200211111111122122220022000001000 201012122221022221220222222222221122022020000000100 201012122102222212202222222222212120220202000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 12 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 210210212222210211200211111111122122220022000001000 201012122221022221220222222222221122022020000000100 201012122102222212202211111111112120220202000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 13 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 210210212222210211200211111111122122220022000001000 201012122221022221220200000000021122022020000000100 201012122102222212202200000000012120220202000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 14 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 210210212222210211200211111111122122220022000001000 000000002100000021021022222222200000000021000000100 000000000021000000000000000000021002102100000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 15 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 210210212222210211200211111111122122220022000001000 000000002100000021021022222222200000000021000000100 000000000021000000000022222222221002102100000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 16 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 210210212222210211200211111111122122220022000001000 000000002100000021021000000000000000000021000000100 000000000021000000000000000000021002102100000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 17 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 201012122222210221220211111111121122022020000001000 111222002111011102210122222222222210011112000000100 222111002210222222222200000000021022121000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 18 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 201012122222210221220211111111121122022020000001000 222111002221022222222222222222221022121000000000100 222111002102222201210222222222211120022221000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 19 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 201012122222210221220211111111121122022020000001000 201012122221022212202222222222212120220202000000100 210210212102222211200222222222222122220022000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 20 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 111222002111110210210222222222122210011121000001000 222111002222102222222222222222221022121000000000100 201012122210222122220222222222221122022002000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 21 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 222111002222210222222222222222221022121000000001000 222111002221022210210222222222211120022221000000100 201012122102222212220222222222221122022020000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 22 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222111000222222222211120022222000010000 210210212222210211200222222222222122220022000001000 201012122221022221220222222222221122022020000000100 201012122102222212202222222222212120220202000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 23 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111002222222221022211111111110222121000000001000 000000002221110000000022222222200000000022000000100 000000002102102100000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 24 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111002222222221022211111111110222121000000001000 000000000000000000000022211100000000000022000000100 000000000000000000000021021021000000000021000000010 000000000000000000000000000000000000000000100000001 ?8 51 3 88888824_8 1 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111002222222221022211111111110222121000000001000 000000000000000000000022211100000000000022000000100 000000000000000000000021021021000000000021000000010 201012121122222002222200000000011222022000100000001 AUT: 3359232 $1z^{0}+10z^{9}+90z^{18}+1244z^{27}+5216z^{36} dd-2$\\ Start matrix 1 8 51 25 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111002222222221022211111111110222121000000001000 000000002221110000000000000000000000000022000000100 000000002102102100000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 26 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111001111111111022222222222210222121000000001000 000000002221110000000000000000000000000022000000100 000000002102102100000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 27 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111002222222221022222222222210222121000000001000 000000002221110000000222222222000000000022000000100 000000002102102100000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 28 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111002222222221022222222222210222121000000001000 000000000000000000000222111000000000000022000000100 000000000000000000000210210210000000000021000000010 000000000000000000000000000000000000000000100000001 ?8 51 3 88888828_8 2 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111002222222221022222222222210222121000000001000 000000000000000000000222111000000000000022000000100 000000000000000000000210210210000000000021000000010 201012121122222002222000000002011222022000100000001 AUT: 10077696 $1z^{0}+12z^{9}+84z^{18}+1250z^{27}+5214z^{36} dd-2$\\ ?8 51 3 88888828_8 3 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111002222222221022222222222210222121000000001000 000000000000000000000222111000000000000022000000100 000000000000000000000210210210000000000021000000010 201012121122222002222222222222211222022000100000001 AUT: 20155392 $1z^{0}+12z^{9}+102z^{18}+1214z^{27}+5232z^{36} dd-2$\\ Start matrix 1 8 51 29 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111002222222221022222222222210222121000000001000 000000002221110000000000000000000000000022000000100 000000002102102100000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 30 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 210210212222211100022222222222221222220022000001000 210210212221021021022222222222221222220021000000100 201012122102221222022222222222211222022020000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 31 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222222210222222222221022121000000010000 210210212222222221022211111111101121022100000001000 000000002221110000000022222222200000000022000000100 000000002102102100000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 32 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222222210222222222221022121000000010000 210210212222222221022211111111101121022100000001000 000000002221110000000000000000000000000022000000100 000000002102102100000000000000000000000021000000010 000000000000000000000000000000000000000000100000001 ?8 51 3 88888832_8 4 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 222111002222222222210222222222221022121000000010000 210210212222222221022211111111101121022100000001000 000000002221110000000000000000000000000022000000100 000000002102102100000000000000000000000021000000010 021102210000000002211211222220022222011000100000001 AUT: 60466176 $1z^{0}+14z^{9}+78z^{18}+1256z^{27}+5212z^{36} dd-2$\\ Start matrix 1 8 51 33 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 111222002222222221211102110221021001212211000001000 222111002222222220022200210210000210000021000000100 210210210000000000021000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 34 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 111222002222222221211102110221021001212211000001000 222111002222222220022200210210000210000021000000100 210210212222222220021000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 35 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 111222002222222221211102110221021001212211000001000 222111000000000000022200210210000210000021000000100 210210210000000000021000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 36 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 111222002222222221211102110221021001212211000001000 222111000000000000022200210210000210000021000000100 210210212222222220021000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 37 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 111222002222222221211102110221021001212211000001000 210210212222222220021000000000000000000000000000100 000000002222222220000000210210000210000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 38 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 111222002222222221211102110221021001212211000001000 000000002222222220000000210210000210000021000000100 210210210000000000021000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 39 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 222111002222222221222202110221021001212211000001000 222111002222222220222000210210000210000021000000100 210210210000000000210000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 40 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 222111002222222221222202110221021001212211000001000 222111002222222220222000210210000210000021000000100 210210212222222220210000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 41 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 222111002222222221222202110221021001212211000001000 222111000000000000222000210210000210000021000000100 210210210000000000210000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 42 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 222111002222222221222202110221021001212211000001000 210210212222222220210000000000000000000000000000100 000000002222222220000000210210000210000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 43 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 222111002222222221222202110221021001212211000001000 000000002222222220000000210210000210000021000000100 210210210000000000210000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 44 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 222111002222222222222102210211021002121221000001000 222111002222222220222002100021000210000210000000100 210210210000000000210000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 45 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 222111002222222222222102210211021002121221000001000 222111000000000000222002100021000210000210000000100 210210210000000000210000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 46 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 222111002000000000222102210211021002121221000001000 222111000222222222222002100021000210000210000000100 210210210000000000210000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 47 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 111222002222222222111102222111100002121222000010000 222111002000000000222102210211021002121221000001000 222111000222222222222002100021000210000210000000100 210210210222222222210000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 48 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 222111002222222222222102222111100002121222000010000 222111002222222222221202110221021001212211000001000 222111002222222222220000210210000210000021000000100 210210212100000000000000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 49 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 222111002222222222222102222111100002121222000010000 222111002222222222221202110221021001212211000001000 222111002222222222220000210210000210000021000000100 210210212222222222100000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 50 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 222111002222222222222102222111100002121222000010000 222111002222222222221202110221021001212211000001000 210210212222222222100000000000000000000000000000100 000000000000000000000000210210000210000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 51 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 222111002222222222222102222111100002121222000010000 222111002222222222221202110221021001212211000001000 210210212100000000000000000000000000000000000000100 000000000000000000000000210210000210000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 52 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 222111002222222222222102222111100002121222000010000 222111002222222222222102210211021002121221000001000 210210212222222222100000000000000000000000000000100 000000000000000000000002100021000210000210000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 53 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 222111002222222222222102222111100002121222000010000 222111002222222222222102210211021002121221000001000 210210212100000000000000000000000000000000000000100 000000000000000000000002100021000210000210000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 54 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 222111002222222111100002222222222102121222000010000 111222002111110221021002222222221201212211000001000 222111000222210210000210000000000000000021000000100 210210210210000000000000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 55 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 222111002222222111100002222222222102121222000010000 111222002111110221021002222222221201212211000001000 210210210210000000000002222222220000000000000000100 000000000002100210000212222222220000000021000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 56 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 222111002222222111100002222222222102121222000010000 111222002111110221021002222222221201212211000001000 000000000210000210000212222222220000000021000000100 210210210002100000000000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 57 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 222111002222222111100002222222222102121222000010000 111222002211110211021002222222222102121221000001000 222111002122200021000210000000000000000210000000100 210210210021000000000000000000000000000000000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 58 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222221111111111110022000000100000 222111002222222222222102222222222102121000000010000 210210212222111100000000000000000000000222000001000 210210212210211021000000000000000000000221000000100 000000002100021000210000000000000000000210000000010 000000000000000000000000000000000000000000100000001 Start matrix 1 8 51 59 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 111222002222222222222221111111110000022222000100000 222111002222222222222102222100002111121111000010000 222111002100000000000002220021000210002100000001000 222111000021000000000002220000210002100021000000100 210210210000000000000002100000000000000000000000010 000000000000000000000000000000000000000000100000001 ?8 51 3 88888859_8 5 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 111222002222222222222221111111110000022222000100000 222111002222222222222102222100002111121111000010000 222111002100000000000002220021000210002100000001000 222111000021000000000002220000210002100021000000100 210210210000000000000002100000000000000000000000010 000000000000112200000000000022110112202211100000001 AUT: 5038848 $1z^{0}+8z^{9}+96z^{18}+1238z^{27}+5218z^{36} dd-2$\\ Start matrix 1 8 51 60 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 222111002222222222222222221111110000022222000100000 222111002222222222222222102100002111121111000010000 210210212100000000000000000022200111002220000001000 120120120021000000000000000022020110102202000000100 000000000000210000000000000021000210002100000000010 000000000000000000000000000000000000000000100000001 Extension: [50,7,9] to [51,8,9] Number of the matrices for extension:143 Weights: 9 18 27 36 45 Maximal number for proportional coordinatesTill dimension 1--51; Till dimension 2--51; Till dimension 3--51; Till dimension 4--51; Till dimension 5--51; Till dimension 6--51; Till dimension 7--51; Till dimension 8--51; The minimum distace of the dual codes is: 2 ============================================ Start matrix 1 8 51 1 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111002222222221022211111111110222121000000001000 201012122222211002222222222222211222022020000000100 000000000000000000000022211100000000000002200000010 000000000000000000000000000000000000000000000000001 ?8 51 3 8888881_8 1 111111110000000000000000000000000000000000010000000 222111002222222222222222222222222222200000001000000 210210212222222222222111111111111100022200000100000 210210212222222222210222222222211021022100000010000 222111002222222221022211111111110222121000000001000 201012122222211002222222222222211222022020000000100 000000000000000000000022211100000000000002200000010 000000000000000000000012012012000000000001200000001 AUT: 3359232 $1z^{0}+10z^{9}+90z^{18}+1244z^{27}+5216z^{36} dd-2$