lower bound: | 31 |
upper bound: | 35 |
Construction of a linear code [88,18,31] over GF(2): [1]: [2, 1, 2] Cyclic Linear Code over GF(2) RepetitionCode of length 2 [2]: [3, 2, 2] Cyclic Linear Code over GF(2) CordaroWagnerCode of length 3 [3]: [84, 17, 30] Quasicyclic of degree 4 Linear Code over GF(2) QuasiCyclicCode of length 84 with generating polynomials: x^20 + x^18 + x^17 + x^16, x^17 + x^16 + x^15 + x^13 + x^10 + x^9 + x^7 + x^3, x^20 + x^19 + x^17 + x^16 + x^15 + x^12 + x^11 + x^8 + x^7 + x^4 + x^2 + x, x^20 + x^19 + x^18 + x^17 + x^16 + x^14 + x^12 + x^8 + x^7 + x^6 + x^5 + x^2 + x + 1 [4]: [84, 16, 30] Quasicyclic of degree 4 Linear Code over GF(2) QuasiCyclicCode of length 84 with generating polynomials: x^19 + x^18 + x^17 + x^16 + x^10, x^19 + x^18 + x^16 + x^10 + x^8 + x^2 + x + 1, x^19 + x^18 + x^17 + x^16 + x^15 + x^13 + x^12 + x^10 + x^9 + x^7 + x^6 + x^5 + x^3 + x, x^16 + x^13 + x^9 + x^7 + x^5 + x^3 + 1 [5]: [84, 18, 28] Quasicyclic of degree 4 Linear Code over GF(2) QuasiCyclicCode of length 84 with generating polynomials: x^20 + x^18 + 1, x^18 + x^16 + x^15 + x^11 + x^8 + x^7 + x^6 + x^5, x^18 + x^16 + x^15 + x^14 + x^12 + x^11 + x^10 + x^8 + x^7 + x^6 + x^3 + 1, x^19 + x^17 + x^16 + x^13 + x^12 + x^11 + x^10 + x^8 + x^6 + x^5 + x^4 + x^2 + 1 [6]: [89, 18, 32] Linear Code over GF(2) ConstructionXX using [5] [4] [3] [2] and [1] [7]: [88, 18, 31] Linear Code over GF(2) Puncturing of [6] at { 89 } last modified: 2016-11-16
Lb(88,18) = 30 is found by truncation of: Lb(90,18) = 32 is found by adding a parity check bit to: Lb(89,18) = 31 BEx Ub(88,18) = 35 is found by considering shortening to: Ub(85,15) = 35 is found by considering truncation to: Ub(84,15) = 34 Ja
Ja: D.B. Jaffe, Binary linear codes: new results on nonexistence, 1996, code.ps.gz.
Notes
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