lower bound: | 56 |
upper bound: | 59 |
Construction of a linear code [80,7,56] over GF(5): [1]: [126, 8, 95] Constacyclic by 2 Linear Code over GF(5) ConstaCyclicCode generated by x^125 + 2*x^124 + 2*x^123 + 3*x^121 + 2*x^119 + 4*x^118 + 4*x^117 + x^116 + 4*x^115 + 4*x^114 + 4*x^113 + 2*x^112 + 2*x^111 + x^110 + 4*x^109 + x^108 + 2*x^107 + 2*x^106 + 3*x^103 + 3*x^102 + 2*x^101 + 3*x^100 + 4*x^99 + 4*x^98 + 2*x^97 + 4*x^94 + 2*x^93 + 4*x^92 + 2*x^91 + 4*x^90 + 3*x^89 + 2*x^88 + 2*x^85 + 3*x^84 + 2*x^83 + 2*x^81 + 3*x^80 + 2*x^79 + 2*x^78 + 3*x^77 + x^76 + 3*x^75 + x^73 + 2*x^71 + 2*x^70 + 2*x^69 + 4*x^67 + 3*x^65 + x^64 + 2*x^63 + 4*x^61 + 3*x^59 + 2*x^58 + 2*x^57 + x^56 + 2*x^55 + x^54 + 3*x^53 + 2*x^51 + x^50 + 3*x^49 + 4*x^46 + 2*x^45 + 2*x^44 + 2*x^43 + 3*x^42 + 3*x^41 + 2*x^40 + 3*x^37 + 2*x^36 + 4*x^35 + x^34 + 3*x^33 + 4*x^32 + 3*x^31 + x^28 + 2*x^27 + 2*x^26 + x^25 + 3*x^24 + 2*x^23 + 4*x^22 + x^21 + 2*x^20 + 4*x^19 + 2*x^18 + x^17 + 2*x^16 + 2*x^15 + 2*x^13 + 2*x^11 + 4*x^10 + 4*x^9 + 4*x^8 + 1 with shift constant 2 [2]: [125, 7, 95] Linear Code over GF(5) Shortening of [1] at { 126 } [3]: [80, 7, 56] Linear Code over GF(5) Puncturing of [2] at { 1, 2, 3, 5, 7, 10, 14, 15, 16, 19, 20, 25, 26, 27, 31, 32, 34, 39, 43, 47, 48, 49, 52, 53, 54, 58, 59, 60, 64, 65, 66, 69, 70, 72, 78, 93, 95, 98, 101, 102, 105, 106, 107, 108, 113 } last modified: 2003-07-08
Lb(80,7) = 56 GW1 Ub(80,7) = 59 DG1
GW1: M. Grassl & G. White, New Good Linear Codes by Special Puncturings, ISIT 2004 Chicago USA June 27 - July 2 2004.
Notes
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