lower bound: | 95 |
upper bound: | 98 |
Construction of a linear code [212,15,95] over GF(2): [1]: [23, 12, 7] "Quadratic Residue code" Linear Code over GF(2) QRCode over GF(2)of length 23 [2]: [23, 11, 8] Cyclic Linear Code over GF(2) Dual of [1] [3]: [19, 7, 8] Linear Code over GF(2) Shortening of [2] at { 20, 21, 22, 23 } [4]: [63, 4, 47] "BCH code (d = 46, b = 1)" Linear Code over GF(2^2) BCHCode over GF(4) with parameters 63 46 [5]: [189, 8, 94] Linear Code over GF(2) ConcatenatedCode of [4] and [16] [6]: [192, 8, 96] Linear Code over GF(2) The Generator Elements of [5] with respect to the basis of [15] encoded to new generator elements using [13] [7]: [194, 8, 96] Linear Code over GF(2) The Generator Elements of [6] with respect to the basis of [20] encoded to new generator elements using [21] [8]: [2, 1, 2] Cyclic Linear Code over GF(2) RepetitionCode of length 2 [9]: [192, 2, 102] Quasicyclic of degree 64 Linear Code over GF(2) CodeComplement of [13] with [19] [10]: [192, 1, 102] Linear Code over GF(2) Subcode of [9] [11]: [63, 7, 43] "BCH code (d = 42, b = 63)" Linear Code over GF(2^2) BCHCode over GF(4) with parameters 63 42 0 [12]: [189, 14, 86] Linear Code over GF(2) ConcatenatedCode of [11] and [16] [13]: [192, 16, 86] Linear Code over GF(2) ConstructionX using [15] [12] and [16] [14]: [63, 8, 42] "BCH code (d = 42, b = 1)" Linear Code over GF(2^2) BCHCode over GF(4) with parameters 63 42 [15]: [189, 16, 84] Linear Code over GF(2) ConcatenatedCode of [14] and [16] [16]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [17]: [63, 7, 43] "BCH code (d = 43, b = 1)" Linear Code over GF(2^2) BCHCode over GF(4) with parameters 63 43 [18]: [189, 14, 86] Linear Code over GF(2) ConcatenatedCode of [17] and [16] [19]: [192, 14, 88] Linear Code over GF(2) The Generator Elements of [18] with respect to the basis of [15] encoded to new generator elements using [13] [20]: [192, 15, 86] Linear Code over GF(2) The Vector space sum: [19] + [10] [21]: [194, 15, 88] Linear Code over GF(2) ConstructionX using [20] [19] and [8] [22]: [213, 15, 96] Linear Code over GF(2) ConstructionX using [21] [7] and [3] [23]: [212, 15, 95] Linear Code over GF(2) Puncturing of [22] at { 213 } last modified: 2001-01-30
Lb(212,15) = 95 is found by truncation of: Lb(213,15) = 96 EB1 Ub(212,15) = 98 is found by considering shortening to: Ub(210,13) = 98 otherwise adding a parity check bit would contradict: Ub(211,13) = 99 BK
EB1: Y. Edel & J. Bierbrauer, Some codes related to BCH codes of low dimension, preprint, 1995.
Notes
|