lower bound: | 106 |
upper bound: | 109 |
Construction of a linear code [232,13,106] over GF(2): [1]: [4, 4, 1] Cyclic Linear Code over GF(2) UniverseCode of length 4 [2]: [15, 2, 14] Linear Code over GF(2^4) Shortening of [5] at { 16 .. 17 } [3]: [225, 9, 105] Linear Code over GF(2) ZinovievCode using inner codes: [9] [8], outer codes: [2] [4] [4]: [15, 1, 15] Cyclic Linear Code over GF(2) RepetitionCode of length 15 [5]: [17, 4, 14] "BCH code (d = 14, b = 11)" Linear Code over GF(2^4) BCHCode over GF(16) with parameters 17 14 11 [6]: [16, 3, 14] Linear Code over GF(2^4) Shortening of [5] at { 17 } [7]: [15, 3, 13] Linear Code over GF(2^4) Puncturing of [6] at { 16 } [8]: [15, 5, 7] "BCH code (d = 7, b = 1)" Linear Code over GF(2) BCHCode with parameters 15 7 [9]: [15, 4, 8] "BCH code (d = 8, b = 15)" Linear Code over GF(2) BCHCode with parameters 15 8 0 [10]: [225, 13, 104] Linear Code over GF(2) ZinovievCode using inner codes: [9] [8], outer codes: [7] [4] [11]: [229, 13, 105] Linear Code over GF(2) ConstructionX using [10] [3] and [1] [12]: [230, 13, 106] Linear Code over GF(2) ExtendCode [11] by 1 [13]: [232, 13, 106] Linear Code over GF(2) PadCode [12] by 2 last modified: 2019-04-09
Lb(232,13) = 106 is found by truncation of: Lb(234,13) = 108 is found by adding a parity check bit to: Lb(233,13) = 107 Gra Ub(232,13) = 110 follows by a one-step Griesmer bound from: Ub(121,12) = 55 Bro
Gra:
Notes
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