lower bound: | 64 |
upper bound: | 68 |
Construction of a linear code [148,13,64] over GF(2): [1]: [24, 12, 8] Linear Code over GF(2) Extend the QRCode over GF(2)of length 23 [2]: [19, 7, 8] Linear Code over GF(2) Shortening of [1] at { 20 .. 24 } [3]: [146, 15, 63] Linear Code over GF(2) Let C1 be the BCHCode over GF( 2) of parameters 127 55. Let C2 the SubcodeBetweenCode of dimension 15 between C1 and the BCHCode with parameters 127 63. Return ConstructionX using C1, C2 and [2] [4]: [147, 15, 64] Linear Code over GF(2) ExtendCode [3] by 1 [5]: [148, 15, 64] Linear Code over GF(2) PadCode [4] by 1 [6]: [148, 13, 64] Linear Code over GF(2) Subcode of [5] last modified: 2001-01-30
Lb(148,13) = 64 is found by taking a subcode of: Lb(148,15) = 64 is found by lengthening of: Lb(147,15) = 64 is found by adding a parity check bit to: Lb(146,15) = 63 X Ub(148,13) = 68 follows by a one-step Griesmer bound from: Ub(79,12) = 34 follows by a one-step Griesmer bound from: Ub(44,11) = 17 follows by a one-step Griesmer bound from: Ub(26,10) = 8 is found by considering shortening to: 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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