lower bound: | 99 |
upper bound: | 100 |
Construction of a linear code [208,10,99] 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]: [62, 4, 53] Linear Code over GF(2^3) Puncturing of [5] at { 1, 2 } [7]: [434, 12, 112] Linear Code over GF(2) ConcatenatedCode of [6] and [4] [8]: [210, 11, 100] Linear Code over GF(2) generalized residue code of [7] puncturing at the support of a word of weight 224 [9]: [209, 11, 99] Linear Code over GF(2) Puncturing of [8] at { 210 } [10]: [208, 10, 99] Linear Code over GF(2) Shortening of [9] at { 209 } last modified: 2001-01-30
Lb(208,10) = 99 is found by shortening of: Lb(209,11) = 99 is found by truncation of: Lb(210,11) = 100 EB1 Ub(208,10) = 100 follows by a one-step Griesmer bound from: Ub(107,9) = 50 follows by a one-step Griesmer bound from: 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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