lower bound: | 28 |
upper bound: | 44 |
Construction of a linear code [109,48,28] over GF(4): [1]: [4, 3, 2] Cyclic Linear Code over GF(2^2) Dual of the RepetitionCode of length 4 [2]: [105, 45, 28] Constacyclic by w Linear Code over GF(2^2) ConstaCyclicCode generated by w^2*x^104 + w*x^103 + w*x^101 + w^2*x^100 + w^2*x^98 + w^2*x^96 + x^95 + w^2*x^94 + w*x^91 + w*x^90 + w^2*x^89 + x^88 + w*x^86 + w*x^85 + w*x^84 + w*x^83 + w^2*x^82 + w*x^81 + w^2*x^80 + x^78 + w^2*x^77 + w*x^76 + w*x^75 + x^74 + w*x^72 + w*x^71 + x^70 + w^2*x^69 + w^2*x^65 + w*x^64 + w^2*x^62 + w^2*x^61 + w*x^60 + w^2*x^57 + x^56 + x^54 + w*x^53 + w*x^49 + x^47 + w^2*x^46 + x^45 + x^36 with shift constant w [3]: [105, 48, 26] Constacyclic by w Linear Code over GF(2^2) ConstaCyclicCode generated by w*x^103 + w*x^102 + w*x^101 + x^100 + x^99 + x^96 + x^95 + x^93 + w^2*x^92 + w^2*x^90 + w*x^88 + x^87 + w*x^86 + w*x^85 + w^2*x^84 + x^82 + w^2*x^81 + w*x^80 + w*x^79 + w^2*x^78 + w*x^75 + x^73 + w*x^72 + w*x^71 + w*x^70 + w^2*x^69 + x^68 + x^67 + w*x^65 + x^64 + w^2*x^62 + x^61 + x^60 + w*x^57 + w*x^54 + w*x^53 + w^2*x^51 + w^2*x^50 + w^2*x^49 + w^2*x^48 + x^17 with shift constant w [4]: [109, 48, 28] Linear Code over GF(2^2) ConstructionX using [3] [2] and [1] last modified: 2020-08-21
Lb(109,48) = 27 is found by shortening of: Lb(112,51) = 27 Var Ub(109,48) = 44 is found by considering shortening to: Ub(91,30) = 44 LP
Var: From the Varshamov-Gilbert bound. Cf. R.R. Varshamov, Problems of the general theory of linear coding, Ph.D. thesis, Moscow State Univ., 1959. (Russian)
Notes
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