lower bound: | 52 |
upper bound: | 53 |
Construction of a linear code [114,10,52] 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]: [224, 11, 108] Linear Code over GF(2) generalized residue code of [6] puncturing at the support of a word of weight 224 [8]: [223, 11, 107] Linear Code over GF(2) Puncturing of [7] at 1 [9]: [116, 10, 54] Linear Code over GF(2) generalized residue code of [8] puncturing at the support of a word of weight 107 [10]: [114, 10, 52] Linear Code over GF(2) Puncturing of [9] at { 115 .. 116 } last modified: 2001-01-30
Lb(114,10) = 52 is found by truncation of: Lb(116,10) = 54 is found by construction A: taking the residue of: Lb(223,11) = 107 is found by truncation of: Lb(224,11) = 108 EB1 Ub(114,10) = 53 follows by a one-step Griesmer bound from: Ub(60,9) = 26 is found by considering shortening to: Ub(59,8) = 26 otherwise adding a parity check bit would contradict: Ub(60,8) = 27 BJV
EB1: Y. Edel & J. Bierbrauer, Some codes related to BCH codes of low dimension, preprint, 1995.
Notes
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