lower bound: | 45 |
upper bound: | 46 |
Construction of a linear code [98,9,45] 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]: [192, 11, 92] Linear Code over GF(2) generalized residue code of [6] puncturing at the support of a word of weight 256 [8]: [100, 10, 46] Linear Code over GF(2) ResidueCode of [7] [9]: [99, 10, 45] Linear Code over GF(2) Puncturing of [8] at { 100 } [10]: [98, 9, 45] Linear Code over GF(2) Shortening of [9] at { 99 } last modified: 2001-01-30
Lb(98,9) = 45 is found by shortening of: Lb(99,10) = 45 is found by truncation of: Lb(100,10) = 46 is found by construction A: taking the residue of: Lb(191,11) = 91 is found by truncation of: Lb(192,11) = 92 EB2 Ub(98,9) = 46 is found by considering shortening to: Ub(97,8) = 46 otherwise adding a parity check bit would contradict: Ub(98,8) = 47 DM
EB2: Y. Edel & J. Bierbrauer, Twisted BCH codes, J. of Combinatorial Designs 5 (1997) 377-389.
Notes
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