lower bound: | 32 |
upper bound: | 32 |
Construction of a linear code [74,10,32] 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]: [70, 10, 31] Linear Code over GF(2) Let C1 be the BCHCode over GF( 2) of parameters 63 27. Let C2 the SubcodeBetweenCode of dimension 10 between C1 and the BCHCode with parameters 63 31. Return ConstructionX using C1, C2 and [4] [6]: [71, 10, 32] Linear Code over GF(2) ExtendCode [5] by 1 [7]: [72, 10, 32] Linear Code over GF(2) PadCode [6] by 1 [8]: [73, 10, 32] Linear Code over GF(2) ExtendCode [7] by 1 [9]: [74, 10, 32] Linear Code over GF(2) ExtendCode [8] by 1 last modified: 2001-02-04
Lb(74,10) = 32 is found by taking a subcode of: Lb(74,11) = 32 is found by adding a parity check bit to: Lb(73,11) = 31 GG1 Ub(74,10) = 32 follows by a one-step Griesmer bound from: Ub(41,9) = 16 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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