Extension: [5,5,1] to [22,5,4] 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--22; Till dimension 2--22; Till dimension 3--22; Till dimension 4--22; Till dimension 5--22; The minimum distance of the dual codes is: 2 ======================== Start matrix 1 23 E 11100000000000000100001 00000000000000000010002 00000000000000000001003 00000000000000000000104 00000000000000000000015 ?5 22 4 _5 1 1110000000000000010000 1233333333333330001000 1231112223333003300100 3122301201223131300010 0003010333123230200001 AUT: 11664 $1z^{0}+3z^{4}+48z^{12}+783z^{16}+189z^{20} dd-3$\\ ?5 22 4 _5 2 1110000000000000010000 1233333333333330001000 1231112223333003300100 3122301201223131300010 0000322313100122300001 AUT: 8640 $1z^{0}+3z^{4}+48z^{12}+783z^{16}+189z^{20} dd-3$\\ ?5 22 4 _5 3 1110000000000000010000 1233333333333330001000 1231112223333003300100 3122301201223131300010 1232033120331122300001 AUT: 34560 $1z^{0}+3z^{4}+60z^{12}+759z^{16}+201z^{20} dd-2$\\ ?5 22 4 _5 4 1110000000000000010000 1233333333333330001000 1231112223333003300100 1231232301230132300010 0000031230010200300001 AUT: 6912 $1z^{0}+3z^{4}+3z^{8}+39z^{12}+792z^{16}+186z^{20} dd-3$\\ ?5 22 4 _5 5 1110000000000000010000 1233333333333330001000 1231112223333003300100 3121001331222233300010 0000000000123000000001 AUT: 41472 $1z^{0}+6z^{4}+12z^{8}+30z^{12}+771z^{16}+204z^{20} dd-2$\\ ?5 22 4 _5 6 1110000000000000010000 1233333333333330001000 1231112223333003300100 3121001331222233300010 0000222103122323000001 AUT: 1152 $1z^{0}+3z^{4}+3z^{8}+63z^{12}+744z^{16}+210z^{20} dd-2$\\ ?5 22 4 _5 7 1110000000000000010000 1233333333333330001000 1231112223333003300100 3121001331222233300010 2310220330230001100001 AUT: 5184 $1z^{0}+3z^{4}+9z^{8}+57z^{12}+738z^{16}+216z^{20} dd-2$\\ ?5 22 4 _5 8 1110000000000000010000 1233333333333330001000 1231112223333003300100 3122332001122133300010 0003231330033123000001 AUT: 432 $1z^{0}+3z^{4}+84z^{12}+711z^{16}+225z^{20} dd-2$\\ ?5 22 4 _5 9 1110000000000000010000 1233333333333330001000 1231112223333003300100 1233301231130223300010 0003322001120133300001 AUT: 2592 $1z^{0}+3z^{4}+84z^{12}+711z^{16}+225z^{20} dd-2$\\ ?5 22 4 _5 10 1110000000000000010000 1233333333333330001000 1231112223333003300100 1233302201112333300010 0000000001230000000001 AUT: 3456 $1z^{0}+6z^{4}+9z^{8}+51z^{12}+738z^{16}+219z^{20} dd-2$\\ ?5 22 4 _5 11 1110000000000000010000 1233333333333330001000 1231112223333003300100 1233302201112333300010 0002201101230333300001 AUT: 576 $1z^{0}+3z^{4}+3z^{8}+87z^{12}+696z^{16}+234z^{20} dd-2$\\ ?5 22 4 _5 12 1110000000000000010000 1233333333333330001000 1231112223333003300100 3123332221333101000010 0000000000123000000001 AUT: 3456 $1z^{0}+6z^{4}+9z^{8}+99z^{12}+642z^{16}+267z^{20} dd-2$\\ ?5 22 4 _5 13 1110000000000000010000 1233333333333330001000 1231112223333003300100 3123332221333101000010 0000001230000000000001 AUT: 1728 $1z^{0}+6z^{4}+9z^{8}+99z^{12}+642z^{16}+267z^{20} dd-2$\\ ?5 22 4 _5 14 1110000000000000010000 1233333333333330001000 1231112223333003300100 3123332221333101000010 2310000002333222200001 AUT: 1296 $1z^{0}+3z^{4}+156z^{12}+567z^{16}+297z^{20} dd-2$\\ ?5 22 4 _5 15 1110000000000000010000 1233333333333330001000 1231112223333003300100 2312233332330301100010 0000001230000000000001 AUT: 15552 $1z^{0}+6z^{4}+12z^{8}+42z^{12}+747z^{16}+216z^{20} dd-2$\\ ?5 22 4 _5 16 1110000000000000010000 1233333333333330001000 1231112223333003300100 1231332331230333000010 0000201002013303000001 AUT: 13824 $1z^{0}+3z^{4}+9z^{8}+45z^{12}+762z^{16}+204z^{20} dd-2$\\ ?5 22 4 _5 17 1110000000000000010000 1233333333333330001000 1231112223333003300100 3123333332333120000010 0000000000123000000001 AUT: 2592 $1z^{0}+6z^{4}+21z^{8}+75z^{12}+654z^{16}+267z^{20} dd-2$\\ ?5 22 4 _5 18 1110000000000000010000 1233333333333330001000 1231112223333003300100 3123333332333120000010 1230000003123000000001 AUT: 1296 $1z^{0}+3z^{4}+27z^{8}+75z^{12}+648z^{16}+270z^{20} dd-2$\\ ?5 22 4 _5 19 1110000000000000010000 1233333333333330001000 1231112223333003300100 1233333333333120000010 0000000001230000000001 AUT: 62208 $1z^{0}+9z^{4}+27z^{8}+39z^{12}+696z^{16}+252z^{20} dd-2$\\ ?5 22 4 _5 20 1110000000000000010000 1233333333333330001000 1231112223333003300100 1233333333333120000010 0000001230000000000001 AUT: 20736 $1z^{0}+9z^{4}+27z^{8}+75z^{12}+624z^{16}+288z^{20} dd-2$\\ ?5 22 4 _5 21 1110000000000000010000 1233333333333330001000 1231112223333003300100 1233333333333120000010 0000001233333000000001 AUT: 1728 $1z^{0}+6z^{4}+12z^{8}+138z^{12}+555z^{16}+312z^{20} dd-2$\\ ?5 22 4 _5 22 1110000000000000010000 1233333333333330001000 1231112223333003300100 1233333333333120000010 1230000001233000000001 AUT: 7776 $1z^{0}+6z^{4}+21z^{8}+87z^{12}+630z^{16}+279z^{20} dd-2$\\ ?5 22 4 _5 23 1110000000000000010000 1233333333333330001000 1231112223333003300100 2312223333333002300010 0000001233333000000001 AUT: 432 $1z^{0}+3z^{4}+9z^{8}+165z^{12}+522z^{16}+324z^{20} dd-2$\\ ?5 22 4 _5 24 1110000000000000010000 1233333333333330001000 2311122222333330000100 3121322330123333000010 3121333220123330300001 AUT: 864 $1z^{0}+3z^{4}+3z^{8}+123z^{12}+624z^{16}+270z^{20} dd-2$\\ ?5 22 4 _5 25 1110000000000000010000 1233333333333330001000 2311122222333330000100 0003311330223303000010 0003300220001100300001 AUT: 864 $1z^{0}+3z^{4}+3z^{8}+123z^{12}+624z^{16}+270z^{20} dd-2$\\ ?5 22 4 _5 26 1110000000000000010000 1233333333333330001000 2311122222333330000100 0003322000110003000010 0000000123001230300001 AUT: 1728 $1z^{0}+3z^{4}+6z^{8}+90z^{12}+681z^{16}+243z^{20} dd-2$\\ ?5 22 4 _5 27 1110000000000000010000 1233333333333330001000 2311122222333330000100 0003322000110003000010 0003300220110000300001 AUT: 1728 $1z^{0}+3z^{4}+9z^{8}+129z^{12}+594z^{16}+288z^{20} dd-2$\\ ?5 22 4 _5 28 1110000000000000010000 1233333333333330001000 3121122233333303000100 1231133322222200300010 0000000012300000000001 AUT: 20736 $1z^{0}+6z^{4}+12z^{8}+114z^{12}+603z^{16}+288z^{20} dd-2$\\ ?5 22 4 _5 29 1110000000000000010000 1233333333333330001000 3121122233333303000100 1231133322222200300010 0000012300000000000001 AUT: 20736 $1z^{0}+6z^{4}+12z^{8}+222z^{12}+387z^{16}+396z^{20} dd-2$\\ ?5 22 4 _5 30 1110000000000000010000 1233333333333330001000 3121122233333303000100 1231133322222200300010 0000012333330000000001 AUT: 864 $1z^{0}+3z^{4}+6z^{8}+162z^{12}+537z^{16}+315z^{20} dd-2$\\ ?5 22 4 _5 31 1110000000000000010000 1233333333333330001000 3121122233333303000100 1231133322222200300010 1230030012300000000001 AUT: 864 $1z^{0}+3z^{4}+15z^{8}+99z^{12}+636z^{16}+270z^{20} dd-2$\\ ?5 22 4 _5 32 1110000000000000010000 1233333333333330001000 3121122233333303000100 1233322311222200300010 0000000000123000000001 AUT: 5184 $1z^{0}+6z^{4}+9z^{8}+75z^{12}+690z^{16}+243z^{20} dd-2$\\ ?5 22 4 _5 33 1110000000000000010000 1233333333333330001000 3121122233333303000100 1233322311222200300010 1230000300123000000001 AUT: 864 $1z^{0}+3z^{4}+12z^{8}+84z^{12}+675z^{16}+249z^{20} dd-2$\\ ?5 22 4 _5 34 1110000000000000010000 1233333333333330001000 3121122233333303000100 1231133322333300300010 0000000000123000000001 AUT: 3456 $1z^{0}+6z^{4}+12z^{8}+90z^{12}+651z^{16}+264z^{20} dd-2$\\ ?5 22 4 _5 35 1110000000000000010000 1233333333333330001000 3121122233333303000100 1231133322333300300010 0000012300000000000001 AUT: 6912 $1z^{0}+6z^{4}+12z^{8}+126z^{12}+579z^{16}+300z^{20} dd-2$\\ ?5 22 4 _5 36 1110000000000000010000 1233333333333330001000 3121122233333303000100 1231133322333300300010 1230030000123000000001 AUT: 576 $1z^{0}+3z^{4}+15z^{8}+75z^{12}+684z^{16}+246z^{20} dd-2$\\ ?5 22 4 _5 37 1110000000000000010000 1233333333333330001000 3121122233333303000100 1233322311333300300010 0000000000123000000001 AUT: 6912 $1z^{0}+6z^{4}+12z^{8}+66z^{12}+699z^{16}+240z^{20} dd-2$\\ ?5 22 4 _5 38 1110000000000000010000 1233333333333330001000 3121122233333303000100 0000000011223300300010 0000012300000000000001 AUT: 62208 $1z^{0}+6z^{4}+12z^{8}+78z^{12}+675z^{16}+252z^{20} dd-2$\\ ?5 22 4 _5 39 1110000000000000010000 1233333333333330001000 1231122333333303000100 1232211333333300300010 0000000123000000000001 AUT: 103680 $1z^{0}+6z^{4}+24z^{8}+90z^{12}+615z^{16}+288z^{20} dd-2$\\ ?5 22 4 _5 40 1110000000000000010000 1233333333333330001000 1231122333333303000100 1232211333333300300010 0000000123333300000001 AUT: 12960 $1z^{0}+3z^{4}+18z^{8}+174z^{12}+477z^{16}+351z^{20} dd-2$\\ ?5 22 4 _5 41 1110000000000000010000 1233333333333330001000 1231122333333303000100 1232211333333300300010 1230000123300000000001 AUT: 12960 $1z^{0}+3z^{4}+27z^{8}+75z^{12}+648z^{16}+270z^{20} dd-2$\\ ?5 22 4 _5 42 1110000000000000010000 1233333333333330001000 1231122333333303000100 1233322113333300300010 0000000001230000000001 AUT: 41472 $1z^{0}+6z^{4}+18z^{8}+60z^{12}+693z^{16}+246z^{20} dd-2$\\ ?5 22 4 _5 43 1110000000000000010000 1233333333333330001000 1231122333333303000100 1233322113333300300010 1230000001233000000001 AUT: 5184 $1z^{0}+3z^{4}+21z^{8}+69z^{12}+678z^{16}+252z^{20} dd-2$\\ ?5 22 4 _5 44 1110000000000000010000 1233333333333330001000 1231222223333330000100 2310000002223333300010 0000000000001230000001 AUT: 5184 $1z^{0}+6z^{4}+12z^{8}+186z^{12}+459z^{16}+360z^{20} dd-2$\\ ?5 22 4 _5 45 1110000000000000010000 1233333333333330001000 1231233333333330000100 2310022233333333300010 0000012300000000000001 AUT: 31104 $1z^{0}+9z^{4}+27z^{8}+219z^{12}+336z^{16}+432z^{20} dd-2$\\ ?5 22 4 _5 46 1110000000000000010000 1233333333300000001000 1231122333030000000100 3122333000313300000010 0000000000000033300001 AUT: 2592 $1z^{0}+6z^{4}+12z^{8}+150z^{12}+531z^{16}+324z^{20} dd-2$\\ ?5 22 4 _5 47 1110000000000000010000 1233333333300000001000 1231122333030000000100 2313322230003300000010 0000000000000033300001 AUT: 5184 $1z^{0}+6z^{4}+12z^{8}+150z^{12}+531z^{16}+324z^{20} dd-2$\\ ?5 22 4 _5 48 1110000000000000010000 1233333333300000001000 3121223333300000000100 1230302222033300000010 0000000000000033300001 AUT: 864 $1z^{0}+6z^{4}+27z^{8}+165z^{12}+456z^{16}+369z^{20} dd-2$\\ ?5 22 4 _5 49 1110000000000000010000 1233333333300000001000 3121223333300000000100 1230302222033300000010 0000003333000033300001 AUT: 144 $1z^{0}+3z^{4}+24z^{8}+192z^{12}+423z^{16}+381z^{20} dd-2$\\ ?5 22 4 _5 50 1110000000000000010000 1233333333300000001000 3121223333300000000100 1230302222033300000010 1230300000000033300001 AUT: 144 $1z^{0}+3z^{4}+33z^{8}+165z^{12}+450z^{16}+372z^{20} dd-2$\\ ?5 22 4 _5 51 1110000000000000010000 1233333333300000001000 3121223333300000000100 1230302222033300000010 1230303333000033300001 AUT: 216 $1z^{0}+3z^{4}+21z^{8}+201z^{12}+414z^{16}+384z^{20} dd-2$\\ ?5 22 4 _5 52 1110000000000000010000 1233333333300000001000 3121223333300000000100 1230300000033300000010 0000000000000033300001 AUT: 1296 $1z^{0}+6z^{4}+39z^{8}+177z^{12}+396z^{16}+405z^{20} dd-2$\\ ?5 22 4 _5 53 1110000000000000010000 1233333333300000001000 3121223333300000000100 1230300000033300000010 0000003333000033300001 AUT: 432 $1z^{0}+3z^{4}+36z^{8}+156z^{12}+459z^{16}+369z^{20} dd-2$\\ ?5 22 4 _5 54 1110000000000000010000 1233333333300000001000 3121223333300000000100 1230300000033300000010 1230300000000033300001 AUT: 432 $1z^{0}+3z^{4}+48z^{8}+168z^{12}+399z^{16}+405z^{20} dd-2$\\ ?5 22 4 _5 55 1110000000000000010000 1233333333300000001000 3121223333300000000100 0000003333033300000010 0000000000000033300001 AUT: 2592 $1z^{0}+6z^{4}+30z^{8}+168z^{12}+441z^{16}+378z^{20} dd-2$\\ ?5 22 4 _5 56 1110000000000000010000 1233333333300000001000 3121223333300000000100 0000003333033300000010 0000003333000033300001 AUT: 1296 $1z^{0}+3z^{4}+30z^{8}+186z^{12}+417z^{16}+387z^{20} dd-2$\\ ?5 22 4 _5 57 1110000000000000010000 1233333333300000001000 3121223333300000000100 0000000000033300000010 0000000000000033300001 AUT: 15552 $1z^{0}+9z^{4}+42z^{8}+162z^{12}+405z^{16}+405z^{20} dd-2$\\ ?5 22 4 _5 58 1110000000000000010000 1233333333300000001000 1231233333300000000100 3120023333033300000010 0000000000000033300001 AUT: 10368 $1z^{0}+9z^{4}+27z^{8}+147z^{12}+480z^{16}+360z^{20} dd-2$\\ ?5 22 4 _5 59 1110000000000000010000 1233333333300000001000 1231233333300000000100 3120023333033300000010 0000003333000033300001 AUT: 1728 $1z^{0}+6z^{4}+12z^{8}+210z^{12}+411z^{16}+384z^{20} dd-2$\\ ?5 22 4 _5 60 1110000000000000010000 1233333333300000001000 1231233333300000000100 3120023333033300000010 1230030000000033300001 AUT: 864 $1z^{0}+6z^{4}+21z^{8}+183z^{12}+438z^{16}+375z^{20} dd-2$\\ ?5 22 4 _5 61 1110000000000000010000 1233333333300000001000 1231233333300000000100 3120023333033300000010 1230032222000033300001 AUT: 10368 $1z^{0}+6z^{4}+9z^{8}+219z^{12}+402z^{16}+387z^{20} dd-2$\\ ?5 22 4 _5 62 1110000000000000010000 1233333333300000001000 1231233333300000000100 1230033333033300000010 0000000000000033300001 AUT: 5184 $1z^{0}+9z^{4}+39z^{8}+159z^{12}+420z^{16}+396z^{20} dd-2$\\ ?5 22 4 _5 63 1110000000000000010000 1233333333300000001000 1231233333300000000100 1230033333033300000010 0000033330000033300001 AUT: 1728 $1z^{0}+6z^{4}+24z^{8}+174z^{12}+447z^{16}+372z^{20} dd-2$\\ ?5 22 4 _5 64 1110000000000000010000 1233333333300000001000 1231233333300000000100 1230033333033300000010 1230030000000033300001 AUT: 1728 $1z^{0}+6z^{4}+33z^{8}+147z^{12}+474z^{16}+363z^{20} dd-2$\\ ?5 22 4 _5 65 1110000000000000010000 1233333333300000001000 1231233333300000000100 1230033333033300000010 1230033333000033300001 AUT: 1728 $1z^{0}+6z^{4}+36z^{8}+186z^{12}+387z^{16}+408z^{20} dd-2$\\ ?5 22 4 _5 66 1110000000000000010000 1233333333300000001000 1231233333300000000100 0000033330033300000010 0000000000000033300001 AUT: 20736 $1z^{0}+9z^{4}+30z^{8}+150z^{12}+465z^{16}+369z^{20} dd-2$\\ ?5 22 4 _5 67 1110000000000000010000 1233333333300000001000 1231233333300000000100 0000033330033300000010 0000033330000033300001 AUT: 10368 $1z^{0}+6z^{4}+18z^{8}+204z^{12}+405z^{16}+390z^{20} dd-2$\\ ?5 22 4 _5 68 1110000000000000010000 1233333333300000001000 1231233333300000000100 0000000000033300000010 0000000000000033300001 AUT: 124416 $1z^{0}+12z^{4}+54z^{8}+156z^{12}+369z^{16}+432z^{20} dd-2$\\ ?5 22 4 _5 69 1110000000000000010000 1233333333300000001000 3122333300033300000100 1233000000000033300010 0000000000000012300001 AUT: 10368 $1z^{0}+6z^{4}+57z^{8}+75z^{12}+546z^{16}+339z^{20} dd-2$\\ ?5 22 4 _5 70 1110000000000000010000 1233333333300000001000 3122333300033300000100 0000000000000033300010 0000000000000012300001 AUT: 155520 $1z^{0}+18z^{4}+45z^{8}+39z^{12}+606z^{16}+315z^{20} dd-2$\\ ?5 22 4 _5 71 1110000000000000010000 1233333333300000001000 1233333300033300000100 1233000000000033300010 0000000000000012300001 AUT: 3456 $1z^{0}+6z^{4}+60z^{8}+66z^{12}+555z^{16}+336z^{20} dd-2$\\ ?5 22 4 _5 72 1110000000000000010000 1233333333300000001000 1233333300033300000100 0000000000000033300010 0000000000000012300001 AUT: 51840 $1z^{0}+18z^{4}+48z^{8}+78z^{12}+519z^{16}+360z^{20} dd-2$\\ ?5 22 4 _5 73 1110000000000000010000 1233333333300000001000 0003333333333300000100 0003333333312300000010 0000000000000033300001 AUT: 10368 $1z^{0}+9z^{4}+75z^{8}+195z^{12}+240z^{16}+504z^{20} dd-2$\\ ?5 22 4 _5 74 1110000000000000010000 1233333333300000001000 0003333333333300000100 0003333333312300000010 0003333333300033300001 AUT: 1728 $1z^{0}+6z^{4}+81z^{8}+195z^{12}+234z^{16}+507z^{20} dd-2$\\ ?5 22 4 _5 75 1110000000000000010000 1233333333300000001000 0003333333333300000100 0000000000000033300010 0000000000000012300001 AUT: 25920 $1z^{0}+18z^{4}+57z^{8}+195z^{12}+258z^{16}+495z^{20} dd-2$\\ ?5 22 4 _5 76 1110000000000000010000 1233333333300000001000 0000000000033300000100 0000000000012300000010 0000000000000033300001 AUT: 155520 $1z^{0}+21z^{4}+99z^{8}+147z^{12}+216z^{16}+540z^{20} dd-2$\\ ?5 22 4 _5 77 1110000000000000010000 0003333333333300001000 0001112223330033000100 0003332201112030300010 1230000000000000000001 AUT: 51840 $1z^{0}+15z^{4}+3z^{8}+87z^{12}+648z^{16}+270z^{20} dd-2$\\ ?5 22 4 _5 78 1110000000000000010000 0003333333333300001000 0001112223330033000100 0003332201112030300010 0000002020002233300001 AUT: 20736 $1z^{0}+3z^{4}+9z^{8}+165z^{12}+522z^{16}+324z^{20} dd-2$\\ ?5 22 4 _5 79 1110000000000000010000 0003333333333300001000 0001112223330033000100 0003332201112030300010 0002000011233030000001 AUT: 3456 $1z^{0}+3z^{4}+6z^{8}+162z^{12}+537z^{16}+315z^{20} dd-2$\\ ?5 22 4 _5 80 1110000000000000010000 0003333333333300001000 0001112223330033000100 0003302231121030300010 1230000000000000000001 AUT: 129600 $1z^{0}+15z^{4}+48z^{12}+735z^{16}+225z^{20} dd-2$\\ ?5 22 4 _5 81 1110000000000000010000 0003333333333300001000 0001112223330033000100 0002223332300023300010 1230000000000000000001 AUT: 38880 $1z^{0}+15z^{4}+3z^{8}+87z^{12}+648z^{16}+270z^{20} dd-2$\\ ?5 22 4 _5 82 1110000000000000010000 0003333333333300001000 0001112223330033000100 0002223332300023300010 0000001233210000300001 AUT: 2592 $1z^{0}+3z^{4}+9z^{8}+165z^{12}+522z^{16}+324z^{20} dd-2$\\ ?5 22 4 _5 83 1110000000000000010000 0003333333333300001000 0001122333333030000100 0002211333333003000010 0000000112233000300001 AUT: 25920 $1z^{0}+3z^{4}+18z^{8}+174z^{12}+477z^{16}+351z^{20} dd-2$\\ ?5 22 4 _5 84 1110000000000000010000 0003333333333300001000 0001122333333030000100 0003322113333003000010 0003322331133000300001 AUT: 6912 $1z^{0}+3z^{4}+18z^{8}+174z^{12}+477z^{16}+351z^{20} dd-2$\\ ?5 22 4 _5 85 1110000000000000010000 0003333333333300001000 0001222223333300000100 0000333302222033300010 1230000000000000000001 AUT: 12960 $1z^{0}+15z^{4}+9z^{8}+165z^{12}+474z^{16}+360z^{20} dd-2$\\ ?5 22 4 _5 86 1110000000000000010000 0003333333333300001000 0001222223333300000100 0000333302222033300010 0000000003333012300001 AUT: 432 $1z^{0}+3z^{4}+27z^{8}+183z^{12}+432z^{16}+378z^{20} dd-2$\\ ?5 22 4 _5 87 1110000000000000010000 0003333333333300001000 0001222223333300000100 0000333301230000000010 0000000000000033300001 AUT: 10368 $1z^{0}+6z^{4}+30z^{8}+168z^{12}+441z^{16}+378z^{20} dd-2$\\ ?5 22 4 _5 88 1110000000000000010000 0003333333333300001000 0001222223333300000100 0000333301230000000010 0000333300000033300001 AUT: 1728 $1z^{0}+3z^{4}+30z^{8}+186z^{12}+417z^{16}+387z^{20} dd-2$\\ ?5 22 4 _5 89 1110000000000000010000 0003333333333300001000 0001222223333300000100 0000000003333033300010 1230000000000000000001 AUT: 12960 $1z^{0}+15z^{4}+12z^{8}+204z^{12}+387z^{16}+405z^{20} dd-2$\\ ?5 22 4 _5 90 1110000000000000010000 0003333333333300001000 0001222223333300000100 1230000000000000000010 0000000000000033300001 AUT: 77760 $1z^{0}+18z^{4}+51z^{8}+117z^{12}+432z^{16}+405z^{20} dd-2$\\ ?5 22 4 _5 91 1110000000000000010000 0003333333333300001000 1230000000000000000100 0000000000000033300010 0000000000000012300001 AUT: 1555200 $1z^{0}+30z^{4}+225z^{8}+3z^{12}+90z^{16}+675z^{20} dd-2$\\ ?5 22 4 _5 92 1110000000000000010000 1233333000000000001000 1231233000000000000100 1230030333000000000010 0000000000333333300001 AUT: 10368 $1z^{0}+6z^{4}+84z^{8}+186z^{12}+243z^{16}+504z^{20} dd-2$\\ ?5 22 4 _5 93 1110000000000000010000 1233333000000000001000 1231233000000000000100 0000000333333300000010 0000000000000033300001 AUT: 62208 $1z^{0}+9z^{4}+78z^{8}+198z^{12}+225z^{16}+513z^{20} dd-2$\\ ?5 22 4 _5 94 1110000000000000010000 1233333000000000001000 1231233000000000000100 0000000333333300000010 0000000333300033300001 AUT: 62208 $1z^{0}+6z^{4}+66z^{8}+60z^{12}+549z^{16}+342z^{20} dd-2$\\ ?5 22 4 _5 95 1110000000000000010000 1233333000000000001000 1233000333000000000100 0000000000333333300010 0000000000123000000001 AUT: 10368 $1z^{0}+6z^{4}+48z^{8}+150z^{12}+423z^{16}+396z^{20} dd-2$\\ ?5 22 4 _5 96 1110000000000000010000 1233333000000000001000 0000000333333300000100 0000000123333300000010 0000000000000033300001 AUT: 62208 $1z^{0}+9z^{4}+51z^{8}+171z^{12}+360z^{16}+432z^{20} dd-2$\\ ?5 22 4 _5 97 1110000000000000010000 1233333000000000001000 0000000333333300000100 0000000000000033300010 0000000000000012300001 AUT: 155520 $1z^{0}+18z^{4}+60z^{8}+234z^{12}+171z^{16}+540z^{20} dd-2$\\ ?5 22 4 _5 98 1110000000000000010000 0003333333000000001000 0001122330300000000100 0000000000033300000010 0000000000000033300001 AUT: 466560 $1z^{0}+9z^{4}+42z^{8}+162z^{12}+405z^{16}+405z^{20} dd-2$\\ ?5 22 4 _5 99 1110000000000000010000 0003333333000000001000 0003333000333000000100 0003300330330300000010 0000000000000033300001 AUT: 72576 $1z^{0}+6z^{4}+30z^{8}+168z^{12}+441z^{16}+378z^{20} dd-2$\\ DIFFERENT ENUMERATORS :98 ALL CODES: 99 1 1 AUT: 11664 $1z^{0}+3z^{4}+48z^{12}+783z^{16}+189z^{20} dd-3$\\ 2 1 AUT: 8640 $1z^{0}+3z^{4}+48z^{12}+783z^{16}+189z^{20} dd-3$\\ 3 1 AUT: 34560 $1z^{0}+3z^{4}+60z^{12}+759z^{16}+201z^{20} dd-2$\\ 4 1 AUT: 6912 $1z^{0}+3z^{4}+3z^{8}+39z^{12}+792z^{16}+186z^{20} dd-3$\\ 5 1 AUT: 41472 $1z^{0}+6z^{4}+12z^{8}+30z^{12}+771z^{16}+204z^{20} dd-2$\\ 6 1 AUT: 1152 $1z^{0}+3z^{4}+3z^{8}+63z^{12}+744z^{16}+210z^{20} dd-2$\\ 7 1 AUT: 5184 $1z^{0}+3z^{4}+9z^{8}+57z^{12}+738z^{16}+216z^{20} dd-2$\\ 8 1 AUT: 432 $1z^{0}+3z^{4}+84z^{12}+711z^{16}+225z^{20} dd-2$\\ 9 1 AUT: 2592 $1z^{0}+3z^{4}+84z^{12}+711z^{16}+225z^{20} dd-2$\\ 10 1 AUT: 3456 $1z^{0}+6z^{4}+9z^{8}+51z^{12}+738z^{16}+219z^{20} dd-2$\\ 11 1 AUT: 576 $1z^{0}+3z^{4}+3z^{8}+87z^{12}+696z^{16}+234z^{20} dd-2$\\ 12 1 AUT: 3456 $1z^{0}+6z^{4}+9z^{8}+99z^{12}+642z^{16}+267z^{20} dd-2$\\ 13 1 AUT: 1728 $1z^{0}+6z^{4}+9z^{8}+99z^{12}+642z^{16}+267z^{20} dd-2$\\ 14 1 AUT: 1296 $1z^{0}+3z^{4}+156z^{12}+567z^{16}+297z^{20} dd-2$\\ 15 1 AUT: 15552 $1z^{0}+6z^{4}+12z^{8}+42z^{12}+747z^{16}+216z^{20} dd-2$\\ 16 1 AUT: 13824 $1z^{0}+3z^{4}+9z^{8}+45z^{12}+762z^{16}+204z^{20} dd-2$\\ 17 1 AUT: 2592 $1z^{0}+6z^{4}+21z^{8}+75z^{12}+654z^{16}+267z^{20} dd-2$\\ 18 1 AUT: 1296 $1z^{0}+3z^{4}+27z^{8}+75z^{12}+648z^{16}+270z^{20} dd-2$\\ 19 1 AUT: 62208 $1z^{0}+9z^{4}+27z^{8}+39z^{12}+696z^{16}+252z^{20} dd-2$\\ 20 1 AUT: 20736 $1z^{0}+9z^{4}+27z^{8}+75z^{12}+624z^{16}+288z^{20} dd-2$\\ 21 1 AUT: 1728 $1z^{0}+6z^{4}+12z^{8}+138z^{12}+555z^{16}+312z^{20} dd-2$\\ 22 1 AUT: 7776 $1z^{0}+6z^{4}+21z^{8}+87z^{12}+630z^{16}+279z^{20} dd-2$\\ 23 1 AUT: 432 $1z^{0}+3z^{4}+9z^{8}+165z^{12}+522z^{16}+324z^{20} dd-2$\\ 24 2 AUT: 864 $1z^{0}+3z^{4}+3z^{8}+123z^{12}+624z^{16}+270z^{20} dd-2$\\ 25 1 AUT: 1728 $1z^{0}+3z^{4}+6z^{8}+90z^{12}+681z^{16}+243z^{20} dd-2$\\ 26 1 AUT: 1728 $1z^{0}+3z^{4}+9z^{8}+129z^{12}+594z^{16}+288z^{20} dd-2$\\ 27 1 AUT: 20736 $1z^{0}+6z^{4}+12z^{8}+114z^{12}+603z^{16}+288z^{20} dd-2$\\ 28 1 AUT: 20736 $1z^{0}+6z^{4}+12z^{8}+222z^{12}+387z^{16}+396z^{20} dd-2$\\ 29 1 AUT: 864 $1z^{0}+3z^{4}+6z^{8}+162z^{12}+537z^{16}+315z^{20} dd-2$\\ 30 1 AUT: 864 $1z^{0}+3z^{4}+15z^{8}+99z^{12}+636z^{16}+270z^{20} dd-2$\\ 31 1 AUT: 5184 $1z^{0}+6z^{4}+9z^{8}+75z^{12}+690z^{16}+243z^{20} dd-2$\\ 32 1 AUT: 864 $1z^{0}+3z^{4}+12z^{8}+84z^{12}+675z^{16}+249z^{20} dd-2$\\ 33 1 AUT: 3456 $1z^{0}+6z^{4}+12z^{8}+90z^{12}+651z^{16}+264z^{20} dd-2$\\ 34 1 AUT: 6912 $1z^{0}+6z^{4}+12z^{8}+126z^{12}+579z^{16}+300z^{20} dd-2$\\ 35 1 AUT: 576 $1z^{0}+3z^{4}+15z^{8}+75z^{12}+684z^{16}+246z^{20} dd-2$\\ 36 1 AUT: 6912 $1z^{0}+6z^{4}+12z^{8}+66z^{12}+699z^{16}+240z^{20} dd-2$\\ 37 1 AUT: 62208 $1z^{0}+6z^{4}+12z^{8}+78z^{12}+675z^{16}+252z^{20} dd-2$\\ 38 1 AUT: 103680 $1z^{0}+6z^{4}+24z^{8}+90z^{12}+615z^{16}+288z^{20} dd-2$\\ 39 1 AUT: 12960 $1z^{0}+3z^{4}+18z^{8}+174z^{12}+477z^{16}+351z^{20} dd-2$\\ 40 1 AUT: 12960 $1z^{0}+3z^{4}+27z^{8}+75z^{12}+648z^{16}+270z^{20} dd-2$\\ 41 1 AUT: 41472 $1z^{0}+6z^{4}+18z^{8}+60z^{12}+693z^{16}+246z^{20} dd-2$\\ 42 1 AUT: 5184 $1z^{0}+3z^{4}+21z^{8}+69z^{12}+678z^{16}+252z^{20} dd-2$\\ 43 1 AUT: 5184 $1z^{0}+6z^{4}+12z^{8}+186z^{12}+459z^{16}+360z^{20} dd-2$\\ 44 1 AUT: 31104 $1z^{0}+9z^{4}+27z^{8}+219z^{12}+336z^{16}+432z^{20} dd-2$\\ 45 1 AUT: 2592 $1z^{0}+6z^{4}+12z^{8}+150z^{12}+531z^{16}+324z^{20} dd-2$\\ 46 1 AUT: 5184 $1z^{0}+6z^{4}+12z^{8}+150z^{12}+531z^{16}+324z^{20} dd-2$\\ 47 1 AUT: 864 $1z^{0}+6z^{4}+27z^{8}+165z^{12}+456z^{16}+369z^{20} dd-2$\\ 48 1 AUT: 144 $1z^{0}+3z^{4}+24z^{8}+192z^{12}+423z^{16}+381z^{20} dd-2$\\ 49 1 AUT: 144 $1z^{0}+3z^{4}+33z^{8}+165z^{12}+450z^{16}+372z^{20} dd-2$\\ 50 1 AUT: 216 $1z^{0}+3z^{4}+21z^{8}+201z^{12}+414z^{16}+384z^{20} dd-2$\\ 51 1 AUT: 1296 $1z^{0}+6z^{4}+39z^{8}+177z^{12}+396z^{16}+405z^{20} dd-2$\\ 52 1 AUT: 432 $1z^{0}+3z^{4}+36z^{8}+156z^{12}+459z^{16}+369z^{20} dd-2$\\ 53 1 AUT: 432 $1z^{0}+3z^{4}+48z^{8}+168z^{12}+399z^{16}+405z^{20} dd-2$\\ 54 1 AUT: 2592 $1z^{0}+6z^{4}+30z^{8}+168z^{12}+441z^{16}+378z^{20} dd-2$\\ 55 1 AUT: 1296 $1z^{0}+3z^{4}+30z^{8}+186z^{12}+417z^{16}+387z^{20} dd-2$\\ 56 1 AUT: 15552 $1z^{0}+9z^{4}+42z^{8}+162z^{12}+405z^{16}+405z^{20} dd-2$\\ 57 1 AUT: 10368 $1z^{0}+9z^{4}+27z^{8}+147z^{12}+480z^{16}+360z^{20} dd-2$\\ 58 1 AUT: 1728 $1z^{0}+6z^{4}+12z^{8}+210z^{12}+411z^{16}+384z^{20} dd-2$\\ 59 1 AUT: 864 $1z^{0}+6z^{4}+21z^{8}+183z^{12}+438z^{16}+375z^{20} dd-2$\\ 60 1 AUT: 10368 $1z^{0}+6z^{4}+9z^{8}+219z^{12}+402z^{16}+387z^{20} dd-2$\\ 61 1 AUT: 5184 $1z^{0}+9z^{4}+39z^{8}+159z^{12}+420z^{16}+396z^{20} dd-2$\\ 62 1 AUT: 1728 $1z^{0}+6z^{4}+24z^{8}+174z^{12}+447z^{16}+372z^{20} dd-2$\\ 63 1 AUT: 1728 $1z^{0}+6z^{4}+33z^{8}+147z^{12}+474z^{16}+363z^{20} dd-2$\\ 64 1 AUT: 1728 $1z^{0}+6z^{4}+36z^{8}+186z^{12}+387z^{16}+408z^{20} dd-2$\\ 65 1 AUT: 20736 $1z^{0}+9z^{4}+30z^{8}+150z^{12}+465z^{16}+369z^{20} dd-2$\\ 66 1 AUT: 10368 $1z^{0}+6z^{4}+18z^{8}+204z^{12}+405z^{16}+390z^{20} dd-2$\\ 67 1 AUT: 124416 $1z^{0}+12z^{4}+54z^{8}+156z^{12}+369z^{16}+432z^{20} dd-2$\\ 68 1 AUT: 10368 $1z^{0}+6z^{4}+57z^{8}+75z^{12}+546z^{16}+339z^{20} dd-2$\\ 69 1 AUT: 155520 $1z^{0}+18z^{4}+45z^{8}+39z^{12}+606z^{16}+315z^{20} dd-2$\\ 70 1 AUT: 3456 $1z^{0}+6z^{4}+60z^{8}+66z^{12}+555z^{16}+336z^{20} dd-2$\\ 71 1 AUT: 51840 $1z^{0}+18z^{4}+48z^{8}+78z^{12}+519z^{16}+360z^{20} dd-2$\\ 72 1 AUT: 10368 $1z^{0}+9z^{4}+75z^{8}+195z^{12}+240z^{16}+504z^{20} dd-2$\\ 73 1 AUT: 1728 $1z^{0}+6z^{4}+81z^{8}+195z^{12}+234z^{16}+507z^{20} dd-2$\\ 74 1 AUT: 25920 $1z^{0}+18z^{4}+57z^{8}+195z^{12}+258z^{16}+495z^{20} dd-2$\\ 75 1 AUT: 155520 $1z^{0}+21z^{4}+99z^{8}+147z^{12}+216z^{16}+540z^{20} dd-2$\\ 76 1 AUT: 51840 $1z^{0}+15z^{4}+3z^{8}+87z^{12}+648z^{16}+270z^{20} dd-2$\\ 77 1 AUT: 20736 $1z^{0}+3z^{4}+9z^{8}+165z^{12}+522z^{16}+324z^{20} dd-2$\\ 78 1 AUT: 3456 $1z^{0}+3z^{4}+6z^{8}+162z^{12}+537z^{16}+315z^{20} dd-2$\\ 79 1 AUT: 129600 $1z^{0}+15z^{4}+48z^{12}+735z^{16}+225z^{20} dd-2$\\ 80 1 AUT: 38880 $1z^{0}+15z^{4}+3z^{8}+87z^{12}+648z^{16}+270z^{20} dd-2$\\ 81 1 AUT: 2592 $1z^{0}+3z^{4}+9z^{8}+165z^{12}+522z^{16}+324z^{20} dd-2$\\ 82 1 AUT: 25920 $1z^{0}+3z^{4}+18z^{8}+174z^{12}+477z^{16}+351z^{20} dd-2$\\ 83 1 AUT: 6912 $1z^{0}+3z^{4}+18z^{8}+174z^{12}+477z^{16}+351z^{20} dd-2$\\ 84 1 AUT: 12960 $1z^{0}+15z^{4}+9z^{8}+165z^{12}+474z^{16}+360z^{20} dd-2$\\ 85 1 AUT: 432 $1z^{0}+3z^{4}+27z^{8}+183z^{12}+432z^{16}+378z^{20} dd-2$\\ 86 1 AUT: 10368 $1z^{0}+6z^{4}+30z^{8}+168z^{12}+441z^{16}+378z^{20} dd-2$\\ 87 1 AUT: 1728 $1z^{0}+3z^{4}+30z^{8}+186z^{12}+417z^{16}+387z^{20} dd-2$\\ 88 1 AUT: 12960 $1z^{0}+15z^{4}+12z^{8}+204z^{12}+387z^{16}+405z^{20} dd-2$\\ 89 1 AUT: 77760 $1z^{0}+18z^{4}+51z^{8}+117z^{12}+432z^{16}+405z^{20} dd-2$\\ 90 1 AUT: 1555200 $1z^{0}+30z^{4}+225z^{8}+3z^{12}+90z^{16}+675z^{20} dd-2$\\ 91 1 AUT: 10368 $1z^{0}+6z^{4}+84z^{8}+186z^{12}+243z^{16}+504z^{20} dd-2$\\ 92 1 AUT: 62208 $1z^{0}+9z^{4}+78z^{8}+198z^{12}+225z^{16}+513z^{20} dd-2$\\ 93 1 AUT: 62208 $1z^{0}+6z^{4}+66z^{8}+60z^{12}+549z^{16}+342z^{20} dd-2$\\ 94 1 AUT: 10368 $1z^{0}+6z^{4}+48z^{8}+150z^{12}+423z^{16}+396z^{20} dd-2$\\ 95 1 AUT: 62208 $1z^{0}+9z^{4}+51z^{8}+171z^{12}+360z^{16}+432z^{20} dd-2$\\ 96 1 AUT: 155520 $1z^{0}+18z^{4}+60z^{8}+234z^{12}+171z^{16}+540z^{20} dd-2$\\ 97 1 AUT: 466560 $1z^{0}+9z^{4}+42z^{8}+162z^{12}+405z^{16}+405z^{20} dd-2$\\ 98 1 AUT: 72576 $1z^{0}+6z^{4}+30z^{8}+168z^{12}+441z^{16}+378z^{20} dd-2$\\