lower bound: | 162 |
upper bound: | 167 |
Construction of a linear code [228,7,162] over GF(4): [1]: [234, 7, 168] Quasicyclic of degree 2 Linear Code over GF(2^2) QuasiCyclicCode of length 234 with generating polynomials: w^2*x^115 + x^114 + w^2*x^111 + w^2*x^110 + x^109 + w^2*x^108 + x^106 + w*x^105 + w^2*x^104 + w^2*x^103 + w^2*x^101 + x^99 + w^2*x^98 + w^2*x^97 + x^96 + x^95 + w^2*x^94 + w*x^92 + w^2*x^91 + x^90 + w^2*x^89 + x^86 + w^2*x^84 + w^2*x^83 + x^81 + w*x^79 + x^78 + w^2*x^77 + x^76 + w^2*x^74 + w^2*x^73 + x^72 + x^71 + x^69 + w^2*x^68 + w*x^66 + x^65 + x^64 + w^2*x^63 + x^62 + w^2*x^61 + x^59 + x^58 + x^55 + w^2*x^54 + w*x^53 + x^52 + x^50 + w^2*x^49 + w^2*x^48 + w^2*x^46 + x^45 + x^44 + w^2*x^43 + w^2*x^41 + w*x^40 + x^38 + w^2*x^36 + x^35 + x^34 + w^2*x^31 + x^29 + w^2*x^28 + w*x^27 + x^24 + x^22 + w^2*x^21 + w^2*x^18 + w^2*x^17 + x^15 + w*x^14 + w^2*x^12 + x^10 + x^9 + w^2*x^8 + x^7 + x^4 + w^2*x^3 + x^2 + w*x + w^2, w^2*x^116 + w^2*x^114 + x^113 + w*x^112 + w*x^111 + w*x^110 + w*x^108 + w*x^106 + w^2*x^105 + w^2*x^104 + x^103 + w^2*x^102 + x^101 + x^98 + x^96 + x^95 + x^94 + w*x^93 + w^2*x^92 + x^91 + w^2*x^90 + x^89 + w*x^87 + w^2*x^86 + w*x^85 + w*x^84 + x^83 + w*x^81 + x^80 + w*x^78 + w*x^76 + x^74 + w^2*x^73 + w^2*x^72 + w^2*x^71 + w*x^70 + w^2*x^69 + w*x^68 + w^2*x^67 + x^64 + x^62 + w*x^61 + w*x^60 + x^59 + w*x^58 + x^57 + x^56 + x^55 + w^2*x^54 + x^52 + x^50 + w*x^49 + w^2*x^48 + w^2*x^46 + w^2*x^45 + x^44 + w*x^43 + w^2*x^42 + x^41 + w*x^40 + w^2*x^39 + w*x^38 + w^2*x^37 + w*x^36 + x^35 + w^2*x^31 + w^2*x^29 + w*x^27 + w*x^26 + x^25 + w*x^24 + x^23 + w^2*x^22 + w^2*x^21 + x^20 + w^2*x^19 + x^18 + x^17 + x^16 + w*x^14 + x^13 + w*x^12 + x^11 + w^2*x^10 + w*x^8 + x^5 + w^2*x^4 + x^2 + w^2*x [2]: [228, 7, 162] Linear Code over GF(2^2) Puncturing of [1] at { 229 .. 234 } last modified: 2002-10-21
Lb(228,7) = 162 is found by truncation of: Lb(234,7) = 168 DaH Ub(228,7) = 167 follows by a one-step Griesmer bound from: Ub(60,6) = 41 follows by a one-step Griesmer bound from: Ub(18,5) = 10 Liz
Liz: P. Lizak, Optimal quaternary linear codes, Ph. D. Thesis, Univ. of Salford, Nov. 1995.
Notes
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