lower bound: | 70 |
upper bound: | 72 |
Construction of a linear code [156,12,70] over GF(2): [1]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [2]: [1, 1, 1] Cyclic Linear Code over GF(2^2) UniverseCode of length 1 over GF(4) [3]: [51, 46] Cyclic Linear Code over GF(2^2) CyclicCode of length 51 with generating polynomial x^5 + w*x^3 + x + w [4]: [51, 5, 35] Cyclic Linear Code over GF(2^2) Dual of [3] [5]: [52, 5, 36] Linear Code over GF(2^2) ExtendCode [4] by 1 [6]: [51, 45] Cyclic Linear Code over GF(2^2) CyclicCode of length 51 with generating polynomial x^6 + w^2*x^5 + w*x^4 + x^3 + x^2 + x + 1 [7]: [51, 6, 34] Cyclic Linear Code over GF(2^2) Dual of [6] [8]: [52, 6, 35] Linear Code over GF(2^2) ExtendCode [7] by 1 [9]: [53, 6, 36] Linear Code over GF(2^2) ConstructionX using [8] [5] and [2] [10]: [52, 6, 35] Linear Code over GF(2^2) Puncturing of [9] at { 53 } [11]: [156, 12, 70] Linear Code over GF(2) ConcatenatedCode of [10] and [1] last modified: 2001-04-06
Lb(156,12) = 70 BZ Ub(156,12) = 72 follows by a one-step Griesmer bound from: Ub(83,11) = 36 is found by considering shortening to: Ub(82,10) = 36 otherwise adding a parity check bit would contradict: Ub(83,10) = 37 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
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