lower bound: | 93 |
upper bound: | 96 |
Construction of a linear code [204,13,93] over GF(2): [1]: [8, 1, 8] Cyclic Linear Code over GF(2) RepetitionCode of length 8 [2]: [4, 1, 4] Cyclic Linear Code over GF(2) RepetitionCode of length 4 [3]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [4]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) PlotkinSum of [3] and [2] [5]: [16, 5, 8] Linear Code over GF(2) PlotkinSum of [4] and [1] [6]: [63, 7, 43] "BCH code (d = 43, b = 1)" Linear Code over GF(2^2) BCHCode over GF(4) with parameters 63 43 [7]: [189, 14, 86] Linear Code over GF(2) ConcatenatedCode of [6] and [10] [8]: [189, 6, 86] Linear Code over GF(2) CodeComplement of [7] with [12] [9]: [189, 5, 86] Linear Code over GF(2) Subcode of [8] [10]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [11]: [63, 4, 47] "BCH code (d = 47, b = 1)" Linear Code over GF(2^2) BCHCode over GF(4) with parameters 63 47 [12]: [189, 8, 94] Linear Code over GF(2) ConcatenatedCode of [11] and [10] [13]: [189, 13, 86] Linear Code over GF(2) The Vector space sum: [12] + [9] [14]: [205, 13, 94] Linear Code over GF(2) ConstructionX using [13] [12] and [5] [15]: [204, 13, 93] Linear Code over GF(2) Puncturing of [14] at { 205 } last modified: 2001-01-30
Lb(204,13) = 93 is found by truncation of: Lb(205,13) = 94 EB1 Ub(204,13) = 96 follows by a one-step Griesmer bound from: Ub(107,12) = 48 follows by a one-step Griesmer bound from: Ub(58,11) = 24 follows by a one-step Griesmer bound from: Ub(33,10) = 12 is found by considering shortening to: Ub(30,7) = 12 otherwise adding a parity check bit would contradict: Ub(31,7) = 13 vT3
vT3: H.C.A. van Tilborg, The smallest length of binary 7-dimensional linear codes with prescribed minimum distance, Discr. Math. 33 (1981) 197-207.
Notes
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