lower bound: | 34 |
upper bound: | 35 |
Construction of a linear code [78,10,34] 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]: [186, 11, 88] Linear Code over GF(2) Puncturing of [7] at { 187, 188, 189, 190, 191, 192 } [9]: [78, 10, 34] Linear Code over GF(2) generalized residue code of [8] puncturing at the support of a word of weight 108 last modified: 2007-07-17
Lb(78,10) = 34 EB2 Ub(78,10) = 35 follows by a one-step Griesmer bound from: Ub(42,9) = 17 follows by a one-step Griesmer bound from: Ub(24,8) = 8 otherwise adding a parity check bit would contradict: Ub(25,8) = 9 YH1
YH1: Øyvind Ytrehus & Tor Helleseth, There is no binary [25,8,10] code, IEEE Trans. Inform. Theory 36 (May 1990) 695-696.
Notes
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