lower bound: | 56 |
upper bound: | 56 |
Construction of a linear code [118,8,56] over GF(2): [1]: [4, 1, 4] Cyclic Linear Code over GF(2) RepetitionCode of length 4 [2]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [3]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) PlotkinSum of [2] and [1] [4]: [7, 3, 4] Linear Code over GF(2) Shortening of [3] at 1 [5]: [64, 4, 55] Linear Code over GF(2^3) BCHCode over GF(8) with parameters 63 54 [6]: [448, 12, 220] Linear Code over GF(2) ConcatenatedCode of [5] and [4] [7]: [228, 11, 110] Linear Code over GF(2) generalized residue code of [6] puncturing at the support of a word of weight 220 [8]: [227, 11, 109] Linear Code over GF(2) Puncturing of [7] at 1 [9]: [118, 10, 55] Linear Code over GF(2) generalized residue code of [8] puncturing at the support of a word of weight 109 [10]: [119, 10, 56] Linear Code over GF(2) ExtendCode [9] by 1 [11]: [118, 9, 56] Linear Code over GF(2) Shortening of [10] at { 119 } [12]: [118, 8, 56] Linear Code over GF(2) Subcode of [11] last modified: 2001-01-30
Lb(118,8) = 56 is found by taking a subcode of: Lb(118,9) = 56 is found by shortening of: Lb(119,10) = 56 is found by adding a parity check bit to: Lb(118,10) = 55 is found by construction A: taking the residue of: Lb(227,11) = 109 is found by truncation of: Lb(228,11) = 110 EB1 Ub(118,8) = 56 otherwise adding a parity check bit would contradict: Ub(119,8) = 57 DMa
EB1: Y. Edel & J. Bierbrauer, Some codes related to BCH codes of low dimension, preprint, 1995.
Notes
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