lower bound: | 48 |
upper bound: | 48 |
Construction of a linear code [104,9,48] 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]: [103, 10, 48] Linear Code over GF(2) generalized residue code of [12] puncturing at the support of a word of weight 96 [14]: [104, 10, 48] Linear Code over GF(2) PadCode [13] by 1 [15]: [104, 9, 48] Linear Code over GF(2) Subcode of [14] last modified: 2001-01-30
Lb(104,9) = 48 is found by taking a subcode of: Lb(104,10) = 48 is found by lengthening of: Lb(103,10) = 48 is found by adding a parity check bit to: Lb(102,10) = 47 is found by construction A: taking the residue of: Lb(195,11) = 93 B2x Ub(104,9) = 48 follows by a one-step Griesmer bound from: Ub(55,8) = 24 follows by a one-step Griesmer bound from: 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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