lower bound: | 68 |
upper bound: | 72 |
Construction of a linear code [158,14,68] 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]: [4, 1, 4] Cyclic Linear Code over GF(2) RepetitionCode of length 4 [4]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [5]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) PlotkinSum of [4] and [3] [6]: [8, 7, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 8 [7]: [16, 11, 4] Linear Code over GF(2) PlotkinSum of [6] and [5] [8]: [15, 11, 3] Linear Code over GF(2) Puncturing of [7] at 1 [9]: [11, 7, 3] Linear Code over GF(2) Shortening of [8] at { 12 .. 15 } [10]: [127, 7, 64] "BCH code (d = 64, b = 65)" Linear Code over GF(2) BCHCode with parameters 127 64 65 [11]: [127, 7, 64] "BCH code (d = 64, b = 73)" Linear Code over GF(2) BCHCode with parameters 127 64 73 [12]: [127, 14, 56] "BCH code (d = 56, b = 73)" Linear Code over GF(2) BCHCode with parameters 127 56 73 [13]: [157, 14, 67] Linear Code over GF(2) ConstructionXX using [12] [11] [10] [9] and [2] [14]: [158, 14, 68] Linear Code over GF(2) ExtendCode [13] by 1 last modified: 2001-01-30
Lb(158,14) = 68 is found by adding a parity check bit to: Lb(157,14) = 67 XX Ub(158,14) = 72 follows by a one-step Griesmer bound from: Ub(85,13) = 36 follows by a one-step Griesmer bound from: Ub(48,12) = 18 follows by a one-step Griesmer bound from: Ub(29,11) = 9 Ja
XX:
Notes
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