lower bound: | 49 |
upper bound: | 50 |
Construction of a linear code [108,10,49] 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]: [63, 4, 54] Linear Code over GF(2^3) Puncturing of [5] at 1 [7]: [441, 12, 116] Linear Code over GF(2) ConcatenatedCode of [6] and [4] [8]: [221, 11, 106] Linear Code over GF(2) generalized residue code of [7] puncturing at the support of a word of weight 220 [9]: [109, 10, 50] Linear Code over GF(2) generalized residue code of [8] puncturing at the support of a word of weight 112 [10]: [108, 10, 49] Linear Code over GF(2) Puncturing of [9] at { 109 } last modified: 2001-01-30
Lb(108,10) = 49 is found by truncation of: Lb(109,10) = 50 EB1 Ub(108,10) = 50 follows by a one-step Griesmer bound from: Ub(57,9) = 24 is found by considering shortening to: Ub(56,8) = 24 otherwise adding a parity check bit would contradict: Ub(57,8) = 25 BJV
EB1: Y. Edel & J. Bierbrauer, Some codes related to BCH codes of low dimension, preprint, 1995.
Notes
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