lower bound: | 56 |
upper bound: | 56 |
Construction of a linear code [120,10,56] 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]: [228, 11, 110] Linear Code over GF(2) generalized residue code of [6] puncturing at the support of a word of weight 220 [8]: [227, 11, 109] Linear Code over GF(2) Puncturing of [7] at 1 [9]: [118, 10, 55] Linear Code over GF(2) generalized residue code of [8] puncturing at the support of a word of weight 109 [10]: [119, 10, 56] Linear Code over GF(2) ExtendCode [9] by 1 [11]: [120, 10, 56] Linear Code over GF(2) PadCode [10] by 1 last modified: 2001-01-30
Lb(120,10) = 56 is found by lengthening of: Lb(119,10) = 56 is found by adding a parity check bit to: Lb(118,10) = 55 is found by construction A: taking the residue of: Lb(227,11) = 109 is found by truncation of: Lb(228,11) = 110 EB1 Ub(120,10) = 56 follows by a one-step Griesmer bound from: Ub(63,9) = 28 follows by a one-step Griesmer bound from: Ub(34,8) = 14 is found by considering shortening to: Ub(33,7) = 14 otherwise adding a parity check bit would contradict: Ub(34,7) = 15 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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