lower bound: | 44 |
upper bound: | 48 |
Construction of a linear code [110,15,44] over GF(2): [1]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [2]: [64, 8, 43] Linear Code over GF(2^2) BCHCode over GF(4) with parameters 63 42 [3]: [192, 16, 86] Linear Code over GF(2) ConcatenatedCode of [2] and [1] [4]: [191, 16, 85] Linear Code over GF(2) Puncturing of [3] at { 192 } [5]: [106, 15, 43] Linear Code over GF(2) generalized residue code of [4] puncturing at the support of a word of weight 85 [6]: [107, 15, 44] Linear Code over GF(2) ExtendCode [5] by 1 [7]: [110, 15, 44] Linear Code over GF(2) PadCode [6] by 3 last modified: 2001-01-30
Lb(110,15) = 44 is found by lengthening of: Lb(107,15) = 44 is found by adding a parity check bit to: Lb(106,15) = 43 is found by construction A: taking the residue of: Lb(191,16) = 85 is found by truncation of: Lb(192,16) = 86 BZ Ub(110,15) = 48 follows by a one-step Griesmer bound from: Ub(61,14) = 24 follows by a one-step Griesmer bound from: Ub(36,13) = 12 is found by considering shortening to: Ub(30,7) = 12 otherwise adding a parity check bit would contradict: Ub(31,7) = 13 vT3
vT3: H.C.A. van Tilborg, The smallest length of binary 7-dimensional linear codes with prescribed minimum distance, Discr. Math. 33 (1981) 197-207.
Notes
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