Extension: [5,5,1] to [21,5,4] Number of the matrices for extension:1 {self-orthogonal no} Number of ones to add in the first row in the generator matrix of the codes: 3 Weights: 4 8 12 16 20 Maximal number for proportional coordinates in the output codes:Till dimension 1--21; Till dimension 2--21; Till dimension 3--21; Till dimension 4--21; Till dimension 5--21; The minimum distance of the dual codes is: 2 ======================== Start matrix 1 22 E 1110000000000000100001 0000000000000000010002 0000000000000000001003 0000000000000000000104 0000000000000000000015 ?5 21 4 _5 1 111000000000000010000 123333333333333001000 231112222233333000100 231231233312223000010 000000012301230300001 AUT: 3888 $1z^{0}+3z^{4}+3z^{8}+135z^{12}+792z^{16}+90z^{20} dd-2$\\ ?5 21 4 _5 2 111000000000000010000 123333333333333001000 231112222233333000100 312132233012333300010 000000000000123000001 AUT: 5184 $1z^{0}+6z^{4}+9z^{8}+123z^{12}+786z^{16}+99z^{20} dd-2$\\ ?5 21 4 _5 3 111000000000000010000 123333333333333001000 231112222233333000100 312132233012333300010 000003020100123300001 AUT: 1296 $1z^{0}+3z^{4}+3z^{8}+123z^{12}+816z^{16}+78z^{20} dd-3$\\ ?5 21 4 _5 4 111000000000000010000 123333333333333001000 231112222233333000100 312132233012333300010 123032310010230300001 AUT: 864 $1z^{0}+3z^{4}+132z^{12}+807z^{16}+81z^{20} dd-3$\\ ?5 21 4 _5 5 111000000000000010000 123333333333333001000 231112222233333000100 123301230012300300010 000330202010010300001 AUT: 3456 $1z^{0}+3z^{4}+3z^{8}+123z^{12}+816z^{16}+78z^{20} dd-3$\\ ?5 21 4 _5 6 111000000000000010000 123333333333333001000 231112222233333000100 123301230012300300010 000332020001100300001 AUT: 1152 $1z^{0}+3z^{4}+3z^{8}+147z^{12}+768z^{16}+102z^{20} dd-2$\\ ?5 21 4 _5 7 111000000000000010000 123333333333333001000 231112222233333000100 000332200011000300010 000000000000123000001 AUT: 6912 $1z^{0}+6z^{4}+12z^{8}+162z^{12}+699z^{16}+144z^{20} dd-2$\\ ?5 21 4 _5 8 111000000000000010000 123333333333333001000 312112223333330300100 231132301233331200010 000000000012300000001 AUT: 31104 $1z^{0}+6z^{4}+9z^{8}+87z^{12}+858z^{16}+63z^{20} dd-3$\\ ?5 21 4 _5 9 111000000000000010000 123333333333333001000 312112223333330300100 231132301233331200010 312212222312302300001 AUT: 5184 $1z^{0}+3z^{4}+9z^{8}+105z^{12}+834z^{16}+72z^{20} dd-3$\\ ?5 21 4 _5 10 111000000000000010000 123333333333333001000 312112223333330300100 123231231222302200010 000020101200033300001 AUT: 1728 $1z^{0}+3z^{4}+3z^{8}+135z^{12}+792z^{16}+90z^{20} dd-2$\\ ?5 21 4 _5 11 111000000000000010000 123333333333333001000 312112223333330300100 123231231222302200010 123000030123000000001 AUT: 10368 $1z^{0}+3z^{4}+12z^{8}+96z^{12}+843z^{16}+69z^{20} dd-3$\\ ?5 21 4 _5 12 111000000000000010000 123333333333333001000 312112223333330300100 123231231222302200010 000312303120333300001 AUT: 41472 $1z^{0}+3z^{4}+132z^{12}+807z^{16}+81z^{20} dd-3$\\ ?5 21 4 _5 13 111000000000000010000 123333333333333001000 312112223333330300100 123231231222302200010 123312333120333300001 AUT: 6912 $1z^{0}+3z^{4}+3z^{8}+123z^{12}+816z^{16}+78z^{20} dd-3$\\ ?5 21 4 _5 14 111000000000000010000 123333333333333001000 312112223333330300100 312122221223302300010 000001230000000000001 AUT: 31104 $1z^{0}+6z^{4}+15z^{8}+93z^{12}+828z^{16}+81z^{20} dd-2$\\ ?5 21 4 _5 15 111000000000000010000 123333333333333001000 312112223333330300100 312122221223302300010 312121303233332300001 AUT: 5184 $1z^{0}+3z^{4}+12z^{8}+108z^{12}+819z^{16}+81z^{20} dd-2$\\ ?5 21 4 _5 16 111000000000000010000 123333333333333001000 312112223333330300100 312121302333332300010 000000000123000000001 AUT: 20736 $1z^{0}+6z^{4}+12z^{8}+90z^{12}+843z^{16}+72z^{20} dd-2$\\ ?5 21 4 _5 17 111000000000000010000 123333333333333001000 312112223333330300100 123132331233303300010 000021002010033300001 AUT: 6912 $1z^{0}+3z^{4}+9z^{8}+129z^{12}+786z^{16}+96z^{20} dd-2$\\ ?5 21 4 _5 18 111000000000000010000 123333333333333001000 312112223333330300100 123132331233303300010 000200100120033300001 AUT: 6912 $1z^{0}+3z^{4}+9z^{8}+117z^{12}+810z^{16}+84z^{20} dd-2$\\ ?5 21 4 _5 19 111000000000000010000 123333333333333001000 312112223333330300100 123132331233303300010 123000300012300000001 AUT: 6912 $1z^{0}+3z^{4}+15z^{8}+87z^{12}+852z^{16}+66z^{20} dd-3$\\ ?5 21 4 _5 20 111000000000000010000 123333333333333001000 312112223333330300100 123132331233303300010 123132333312033300001 AUT: 20736 $1z^{0}+3z^{4}+9z^{8}+117z^{12}+810z^{16}+84z^{20} dd-2$\\ ?5 21 4 _5 21 111000000000000010000 123333333333333001000 312112223333330300100 123132331233303300010 312132233312033300001 AUT: 27648 $1z^{0}+3z^{4}+6z^{8}+114z^{12}+825z^{16}+75z^{20} dd-3$\\ ?5 21 4 _5 22 111000000000000010000 123333333333333001000 312112223333330300100 123003001230000000010 000000000001230000001 AUT: 10368 $1z^{0}+6z^{4}+21z^{8}+99z^{12}+798z^{16}+99z^{20} dd-2$\\ ?5 21 4 _5 23 111000000000000010000 123333333333333001000 312112223333330300100 123003001230000000010 123003000001230000001 AUT: 6912 $1z^{0}+3z^{4}+27z^{8}+99z^{12}+792z^{16}+102z^{20} dd-2$\\ ?5 21 4 _5 24 111000000000000010000 123333333333333001000 312112223333330300100 000001230000000000010 000000001230000000001 AUT: 62208 $1z^{0}+9z^{4}+27z^{8}+87z^{12}+792z^{16}+108z^{20} dd-2$\\ ?5 21 4 _5 25 111000000000000010000 123333333333333001000 123112233333330300100 123132312333303300010 000000000123000000001 AUT: 497664 $1z^{0}+6z^{4}+18z^{8}+60z^{12}+885z^{16}+54z^{20} dd-3$\\ ?5 21 4 _5 26 111000000000000010000 123333333333333001000 123112233333330300100 123132312333303300010 000021020100033300001 AUT: 96768 $1z^{0}+3z^{4}+21z^{8}+105z^{12}+798z^{16}+96z^{20} dd-2$\\ ?5 21 4 _5 27 111000000000000010000 123333333333333001000 123112233333330300100 123132312333303300010 123000000123300000001 AUT: 62208 $1z^{0}+3z^{4}+21z^{8}+81z^{12}+846z^{16}+72z^{20} dd-2$\\ ?5 21 4 _5 28 111000000000000010000 123333333333333001000 123112233333330300100 123132312333303300010 123132333123033300001 AUT: 331776 $1z^{0}+3z^{4}+18z^{8}+78z^{12}+861z^{16}+63z^{20} dd-3$\\ ?5 21 4 _5 29 111000000000000010000 123333333333333001000 123112233333330300100 123000012330000000010 000000000001230000001 AUT: 31104 $1z^{0}+6z^{4}+24z^{8}+102z^{12}+783z^{16}+108z^{20} dd-2$\\ ?5 21 4 _5 30 111000000000000010000 123333333333333001000 123112233333330300100 123000012330000000010 123000000301230000001 AUT: 20736 $1z^{0}+3z^{4}+30z^{8}+90z^{12}+801z^{16}+99z^{20} dd-2$\\ ?5 21 4 _5 31 111000000000000010000 123333333333333001000 123112233333330300100 000000012300000000010 000000000012300000001 AUT: 746496 $1z^{0}+9z^{4}+30z^{8}+54z^{12}+849z^{16}+81z^{20} dd-2$\\ ?5 21 4 _5 32 111000000000000010000 123333333330000001000 123112233303000000100 123221133300300000010 000000000000033300001 AUT: 25920 $1z^{0}+6z^{4}+24z^{8}+210z^{12}+567z^{16}+216z^{20} dd-2$\\ ?5 21 4 _5 33 111000000000000010000 123333333330000001000 123112233303000000100 123221133300300000010 123000030000033300001 AUT: 4320 $1z^{0}+3z^{4}+27z^{8}+195z^{12}+600z^{16}+198z^{20} dd-2$\\ ?5 21 4 _5 34 111000000000000010000 123333333330000001000 123112233303000000100 123332211300300000010 000000000000033300001 AUT: 10368 $1z^{0}+6z^{4}+18z^{8}+204z^{12}+597z^{16}+198z^{20} dd-2$\\ ?5 21 4 _5 35 111000000000000010000 123333333330000001000 123112233303000000100 123332211300300000010 123000000300033300001 AUT: 1728 $1z^{0}+3z^{4}+21z^{8}+213z^{12}+582z^{16}+204z^{20} dd-2$\\ ?5 21 4 _5 36 111000000000000010000 123333333330000001000 123123333330000000100 231002223333300000010 000000000000033300001 AUT: 31104 $1z^{0}+9z^{4}+27z^{8}+195z^{12}+576z^{16}+216z^{20} dd-2$\\ ?5 21 4 _5 37 111000000000000010000 123333333330000001000 231222333003300000100 000000000000033300010 000000000000012300001 AUT: 311040 $1z^{0}+18z^{4}+45z^{8}+51z^{12}+774z^{16}+135z^{20} dd-2$\\ ?5 21 4 _5 38 111000000000000010000 123333333330000001000 312233330003330000100 123322002202203000010 000000333303300300001 AUT: 6912 $1z^{0}+3z^{4}+6z^{8}+210z^{12}+633z^{16}+171z^{20} dd-2$\\ ?5 21 4 _5 39 111000000000000010000 123333333330000001000 312233330003330000100 123322002202203000010 123300333303300300001 AUT: 1728 $1z^{0}+3z^{4}+9z^{8}+201z^{12}+642z^{16}+168z^{20} dd-2$\\ ?5 21 4 _5 40 111000000000000010000 123333333330000001000 123333330003330000100 123333003303303000010 000000333303300300001 AUT: 12096 $1z^{0}+3z^{4}+21z^{8}+189z^{12}+630z^{16}+180z^{20} dd-2$\\ ?5 21 4 _5 41 111000000000000010000 123333333330000001000 123333330003330000100 123333003303303000010 123300333303300300001 AUT: 13824 $1z^{0}+3z^{4}+18z^{8}+174z^{12}+669z^{16}+159z^{20} dd-2$\\ ?5 21 4 _5 42 111000000000000010000 000333333333330001000 000111222333003300100 000230123130122300010 123000000000000000001 AUT: 6220800 $1z^{0}+15z^{4}+60z^{12}+903z^{16}+45z^{20} dd-3$\\ ?5 21 4 _5 43 111000000000000010000 000333333333330001000 000111222333003300100 000230123130122300010 000032321103213200001 AUT: 293760 $1z^{0}+3z^{4}+204z^{12}+663z^{16}+153z^{20} dd-2$\\ ?5 21 4 _5 44 111000000000000010000 000333333333330001000 000111222333003300100 000330123110223300010 123000000000000000001 AUT: 207360 $1z^{0}+15z^{4}+3z^{8}+99z^{12}+816z^{16}+90z^{20} dd-2$\\ ?5 21 4 _5 45 111000000000000010000 000333333333330001000 000112233333303000100 000221133333300300010 123000000000000000001 AUT: 129600 $1z^{0}+15z^{4}+15z^{8}+255z^{12}+468z^{16}+270z^{20} dd-2$\\ ?5 21 4 _5 46 111000000000000010000 000333333333330001000 000112233333303000100 000332211333300300010 123000000000000000001 AUT: 51840 $1z^{0}+15z^{4}+9z^{8}+177z^{12}+642z^{16}+180z^{20} dd-2$\\ ?5 21 4 _5 47 111000000000000010000 000333333333330001000 000112233333303000100 000000011223300300010 123000000000000000001 AUT: 622080 $1z^{0}+15z^{4}+6z^{8}+138z^{12}+729z^{16}+135z^{20} dd-2$\\ ?5 21 4 _5 48 111000000000000010000 123333300000000001000 123300033300000000100 123300000033300000010 000000000000033300001 AUT: 2592 $1z^{0}+6z^{4}+54z^{8}+240z^{12}+417z^{16}+306z^{20} dd-2$\\ ?5 21 4 _5 49 111000000000000010000 123333300000000001000 123300033300000000100 123300000033300000010 123300000000033300001 AUT: 1728 $1z^{0}+3z^{4}+66z^{8}+222z^{12}+429z^{16}+303z^{20} dd-2$\\ ?5 21 4 _5 50 111000000000000010000 123333300000000001000 123300033300000000100 000000000033300000010 000000000000033300001 AUT: 10368 $1z^{0}+9z^{4}+54z^{8}+222z^{12}+441z^{16}+297z^{20} dd-2$\\ ?5 21 4 _5 51 111000000000000010000 123333300000000001000 000000033333330000100 000000011223303000010 000000033221100300001 AUT: 155520 $1z^{0}+3z^{4}+57z^{8}+153z^{12}+594z^{16}+216z^{20} dd-2$\\ ?5 21 4 _5 52 111000000000000010000 123333300000000001000 000000033300000000100 000000000033300000010 000000000000033300001 AUT: 93312 $1z^{0}+12z^{4}+66z^{8}+216z^{12}+405z^{16}+324z^{20} dd-2$\\ ?5 21 4 _5 53 111000000000000010000 000333333300000001000 000333300033300000100 000333300000033300010 123000000000000000001 AUT: 51840 $1z^{0}+15z^{4}+18z^{8}+294z^{12}+381z^{16}+315z^{20} dd-2$\\ ?5 21 4 _5 54 111000000000000010000 000333333300000001000 000333300033300000100 123000000000000000010 000000000000033300001 AUT: 77760 $1z^{0}+18z^{4}+54z^{8}+168z^{12}+513z^{16}+270z^{20} dd-2$\\ ?5 21 4 _5 55 111000000000000010000 000333333300000001000 123000000000000000100 000000000033300000010 000000000000033300001 AUT: 155520 $1z^{0}+21z^{4}+102z^{8}+198z^{12}+297z^{16}+405z^{20} dd-2$\\ DIFFERENT ENUMERATORS :55 ALL CODES: 55 1 1 AUT: 3888 $1z^{0}+3z^{4}+3z^{8}+135z^{12}+792z^{16}+90z^{20} dd-2$\\ 2 1 AUT: 5184 $1z^{0}+6z^{4}+9z^{8}+123z^{12}+786z^{16}+99z^{20} dd-2$\\ 3 1 AUT: 1296 $1z^{0}+3z^{4}+3z^{8}+123z^{12}+816z^{16}+78z^{20} dd-3$\\ 4 1 AUT: 864 $1z^{0}+3z^{4}+132z^{12}+807z^{16}+81z^{20} dd-3$\\ 5 1 AUT: 3456 $1z^{0}+3z^{4}+3z^{8}+123z^{12}+816z^{16}+78z^{20} dd-3$\\ 6 1 AUT: 1152 $1z^{0}+3z^{4}+3z^{8}+147z^{12}+768z^{16}+102z^{20} dd-2$\\ 7 1 AUT: 6912 $1z^{0}+6z^{4}+12z^{8}+162z^{12}+699z^{16}+144z^{20} dd-2$\\ 8 1 AUT: 31104 $1z^{0}+6z^{4}+9z^{8}+87z^{12}+858z^{16}+63z^{20} dd-3$\\ 9 1 AUT: 5184 $1z^{0}+3z^{4}+9z^{8}+105z^{12}+834z^{16}+72z^{20} dd-3$\\ 10 1 AUT: 1728 $1z^{0}+3z^{4}+3z^{8}+135z^{12}+792z^{16}+90z^{20} dd-2$\\ 11 1 AUT: 10368 $1z^{0}+3z^{4}+12z^{8}+96z^{12}+843z^{16}+69z^{20} dd-3$\\ 12 1 AUT: 41472 $1z^{0}+3z^{4}+132z^{12}+807z^{16}+81z^{20} dd-3$\\ 13 1 AUT: 6912 $1z^{0}+3z^{4}+3z^{8}+123z^{12}+816z^{16}+78z^{20} dd-3$\\ 14 1 AUT: 31104 $1z^{0}+6z^{4}+15z^{8}+93z^{12}+828z^{16}+81z^{20} dd-2$\\ 15 1 AUT: 5184 $1z^{0}+3z^{4}+12z^{8}+108z^{12}+819z^{16}+81z^{20} dd-2$\\ 16 1 AUT: 20736 $1z^{0}+6z^{4}+12z^{8}+90z^{12}+843z^{16}+72z^{20} dd-2$\\ 17 1 AUT: 6912 $1z^{0}+3z^{4}+9z^{8}+129z^{12}+786z^{16}+96z^{20} dd-2$\\ 18 1 AUT: 6912 $1z^{0}+3z^{4}+9z^{8}+117z^{12}+810z^{16}+84z^{20} dd-2$\\ 19 1 AUT: 6912 $1z^{0}+3z^{4}+15z^{8}+87z^{12}+852z^{16}+66z^{20} dd-3$\\ 20 1 AUT: 20736 $1z^{0}+3z^{4}+9z^{8}+117z^{12}+810z^{16}+84z^{20} dd-2$\\ 21 1 AUT: 27648 $1z^{0}+3z^{4}+6z^{8}+114z^{12}+825z^{16}+75z^{20} dd-3$\\ 22 1 AUT: 10368 $1z^{0}+6z^{4}+21z^{8}+99z^{12}+798z^{16}+99z^{20} dd-2$\\ 23 1 AUT: 6912 $1z^{0}+3z^{4}+27z^{8}+99z^{12}+792z^{16}+102z^{20} dd-2$\\ 24 1 AUT: 62208 $1z^{0}+9z^{4}+27z^{8}+87z^{12}+792z^{16}+108z^{20} dd-2$\\ 25 1 AUT: 497664 $1z^{0}+6z^{4}+18z^{8}+60z^{12}+885z^{16}+54z^{20} dd-3$\\ 26 1 AUT: 96768 $1z^{0}+3z^{4}+21z^{8}+105z^{12}+798z^{16}+96z^{20} dd-2$\\ 27 1 AUT: 62208 $1z^{0}+3z^{4}+21z^{8}+81z^{12}+846z^{16}+72z^{20} dd-2$\\ 28 1 AUT: 331776 $1z^{0}+3z^{4}+18z^{8}+78z^{12}+861z^{16}+63z^{20} dd-3$\\ 29 1 AUT: 31104 $1z^{0}+6z^{4}+24z^{8}+102z^{12}+783z^{16}+108z^{20} dd-2$\\ 30 1 AUT: 20736 $1z^{0}+3z^{4}+30z^{8}+90z^{12}+801z^{16}+99z^{20} dd-2$\\ 31 1 AUT: 746496 $1z^{0}+9z^{4}+30z^{8}+54z^{12}+849z^{16}+81z^{20} dd-2$\\ 32 1 AUT: 25920 $1z^{0}+6z^{4}+24z^{8}+210z^{12}+567z^{16}+216z^{20} dd-2$\\ 33 1 AUT: 4320 $1z^{0}+3z^{4}+27z^{8}+195z^{12}+600z^{16}+198z^{20} dd-2$\\ 34 1 AUT: 10368 $1z^{0}+6z^{4}+18z^{8}+204z^{12}+597z^{16}+198z^{20} dd-2$\\ 35 1 AUT: 1728 $1z^{0}+3z^{4}+21z^{8}+213z^{12}+582z^{16}+204z^{20} dd-2$\\ 36 1 AUT: 31104 $1z^{0}+9z^{4}+27z^{8}+195z^{12}+576z^{16}+216z^{20} dd-2$\\ 37 1 AUT: 311040 $1z^{0}+18z^{4}+45z^{8}+51z^{12}+774z^{16}+135z^{20} dd-2$\\ 38 1 AUT: 6912 $1z^{0}+3z^{4}+6z^{8}+210z^{12}+633z^{16}+171z^{20} dd-2$\\ 39 1 AUT: 1728 $1z^{0}+3z^{4}+9z^{8}+201z^{12}+642z^{16}+168z^{20} dd-2$\\ 40 1 AUT: 12096 $1z^{0}+3z^{4}+21z^{8}+189z^{12}+630z^{16}+180z^{20} dd-2$\\ 41 1 AUT: 13824 $1z^{0}+3z^{4}+18z^{8}+174z^{12}+669z^{16}+159z^{20} dd-2$\\ 42 1 AUT: 6220800 $1z^{0}+15z^{4}+60z^{12}+903z^{16}+45z^{20} dd-3$\\ 43 1 AUT: 293760 $1z^{0}+3z^{4}+204z^{12}+663z^{16}+153z^{20} dd-2$\\ 44 1 AUT: 207360 $1z^{0}+15z^{4}+3z^{8}+99z^{12}+816z^{16}+90z^{20} dd-2$\\ 45 1 AUT: 129600 $1z^{0}+15z^{4}+15z^{8}+255z^{12}+468z^{16}+270z^{20} dd-2$\\ 46 1 AUT: 51840 $1z^{0}+15z^{4}+9z^{8}+177z^{12}+642z^{16}+180z^{20} dd-2$\\ 47 1 AUT: 622080 $1z^{0}+15z^{4}+6z^{8}+138z^{12}+729z^{16}+135z^{20} dd-2$\\ 48 1 AUT: 2592 $1z^{0}+6z^{4}+54z^{8}+240z^{12}+417z^{16}+306z^{20} dd-2$\\ 49 1 AUT: 1728 $1z^{0}+3z^{4}+66z^{8}+222z^{12}+429z^{16}+303z^{20} dd-2$\\ 50 1 AUT: 10368 $1z^{0}+9z^{4}+54z^{8}+222z^{12}+441z^{16}+297z^{20} dd-2$\\ 51 1 AUT: 155520 $1z^{0}+3z^{4}+57z^{8}+153z^{12}+594z^{16}+216z^{20} dd-2$\\ 52 1 AUT: 93312 $1z^{0}+12z^{4}+66z^{8}+216z^{12}+405z^{16}+324z^{20} dd-2$\\ 53 1 AUT: 51840 $1z^{0}+15z^{4}+18z^{8}+294z^{12}+381z^{16}+315z^{20} dd-2$\\ 54 1 AUT: 77760 $1z^{0}+18z^{4}+54z^{8}+168z^{12}+513z^{16}+270z^{20} dd-2$\\ 55 1 AUT: 155520 $1z^{0}+21z^{4}+102z^{8}+198z^{12}+297z^{16}+405z^{20} dd-2$\\