lower bound: | 119 |
upper bound: | 120 |
Construction of a linear code [248,10,119] over GF(2): [1]: [51, 8, 24] Cyclic Linear Code over GF(2) CyclicCode of length 51 with generating polynomial x^43 + x^42 + x^41 + x^37 + x^36 + x^33 + x^30 + x^29 + x^27 + x^26 + x^25 + x^22 + x^21 + x^20 + x^19 + x^17 + x^16 + x^13 + x^12 + x^10 + x^7 + x^5 + x^4 + 1 [2]: [6, 2, 4] Quasicyclic of degree 3 Linear Code over GF(2) CordaroWagnerCode of length 6 [3]: [192, 2, 128] Cyclic Linear Code over GF(2) SubcodeWordsOfWeight using weight { 0, 128 } words of [11] [4]: [192, 8, 96] Linear Code over GF(2) SubcodeWordsOfWeight using weight { 0, 96, 128 } words of [11] [5]: [4, 1, 4] Cyclic Linear Code over GF(2) RepetitionCode of length 4 [6]: [4, 3, 2] Cyclic Linear Code over GF(2) Dual of the RepetitionCode of length 4 [7]: [8, 4, 4] Quasicyclic of degree 2 Linear Code over GF(2) PlotkinSum of [6] and [5] [8]: [7, 3, 4] Linear Code over GF(2) Shortening of [7] at 1 [9]: [64, 4, 55] Linear Code over GF(2^3) BCHCode over GF(8) with parameters 63 54 [10]: [448, 12, 220] Linear Code over GF(2) ConcatenatedCode of [9] and [8] [11]: [192, 11, 92] Linear Code over GF(2) generalized residue code of [10] puncturing at the support of a word of weight 256 [12]: [192, 10, 92] Linear Code over GF(2) SubcodeBetweenCode of dimension 10 of [11] and [4] [13]: [249, 10, 120] Linear Code over GF(2) ConstructionXX using [12] [4] [3] [2] and [1] [14]: [248, 10, 119] Linear Code over GF(2) Puncturing of [13] at { 249 } last modified: 2001-04-27
Lb(248,10) = 119 EB2 Ub(248,10) = 120 follows by a one-step Griesmer bound from: Ub(127,9) = 60 follows by a one-step Griesmer bound from: Ub(66,8) = 30 otherwise adding a parity check bit would contradict: Ub(67,8) = 31 DHM
EB2: Y. Edel & J. Bierbrauer, Twisted BCH codes, J. of Combinatorial Designs 5 (1997) 377-389.
Notes
|