lower bound: | 96 |
upper bound: | 96 |
Construction of a linear code [200,9,96] over GF(2): [1]: [7, 4, 3] Linear Code over GF(2) Puncturing of [6] at 1 [2]: [6, 3, 3] Linear Code over GF(2) Shortening of [1] at 1 [3]: [192, 8, 96] Linear Code over GF(2) SubcodeWordsOfWeight using weight { 0, 96, 128 } words of [10] [4]: [4, 1, 4] Cyclic Linear Code over GF(2) RepetitionCode of length 4 [5]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [6]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) PlotkinSum of [5] and [4] [7]: [7, 3, 4] Linear Code over GF(2) Shortening of [6] at 1 [8]: [64, 4, 55] Linear Code over GF(2^3) BCHCode over GF(8) with parameters 63 54 [9]: [448, 12, 220] Linear Code over GF(2) ConcatenatedCode of [8] and [7] [10]: [192, 11, 92] Linear Code over GF(2) generalized residue code of [9] puncturing at the support of a word of weight 256 [11]: [198, 11, 95] Linear Code over GF(2) ConstructionX using [10] [3] and [2] [12]: [199, 11, 96] Linear Code over GF(2) ExtendCode [11] by 1 [13]: [200, 11, 96] Linear Code over GF(2) PadCode [12] by 1 [14]: [200, 9, 96] Linear Code over GF(2) Subcode of [13] last modified: 2001-01-30
Lb(200,9) = 96 is found by taking a subcode of: Lb(200,11) = 96 is found by lengthening of: Lb(199,11) = 96 is found by adding a parity check bit to: Lb(198,11) = 95 EB2 Ub(200,9) = 96 follows by a one-step Griesmer bound from: Ub(103,8) = 48 follows by a one-step Griesmer bound from: Ub(54,7) = 24 otherwise adding a parity check bit would contradict: Ub(55,7) = 25 vT4
vT4: H.C.A. van Tilborg, A proof of the nonexistence of a binary (55,7,26) code, TH-Report 79-WSK-09, Techn. Hogeschool Eindhoven, Nov. 1979.
Notes
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