lower bound: | 149 |
upper bound: | 151 |
Construction of a linear code [231,7,149] over GF(3): [1]: [2, 1, 2] Cyclic Linear Code over GF(3) RepetitionCode of length 2 [2]: [234, 6, 153] Quasicyclic of degree 18 Linear Code over GF(3) QuasiCyclicCode of length 234 with generating polynomials: 2*x^11 + x^9 + 2*x^8 + x^7 + 2*x^6 + 1, 2*x^12 + 2*x^10 + x^6 + x^5 + 2*x^3 + 1, x^11 + x^10 + x^7 + 2*x^6 + 2*x^2 + 2, 2*x^11 + x^10 + 2*x^8 + 2*x^7 + 2*x^6 + x^5 + 2*x^2 + 2*x + 1, x^11 + x^10 + x^9 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^2 + 2*x, 2*x^10 + x^7 + x^4 + x^2 + 2*x + 2, 2*x^12 + x^11 + x^8 + 2*x^7 + 2*x^6 + x^4 + 2*x^3 + 2*x^2 + 2, x^11 + x^9 + x^8 + 2*x^7 + x^6 + x^4 + x^3 + 2*x^2 + 2*x, 2*x^12 + x^11 + 2*x^9 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + x + 2, 2*x^10 + 2*x^9 + 2*x^8 + 2*x^7 + x^6 + 2*x^5 + x^4 + x^2 + 2, x^12 + x^11 + 2*x^10 + x^9 + x^8 + x^3 + 2*x^2 + 2*x + 1, 2*x^10 + x^8 + 2*x^6 + x^5 + 2*x^4 + x^3, 2*x^12 + 2*x^11 + 2*x^10 + 2*x^9 + 2*x^6 + 2*x^5 + 2*x^3 + 2*x + 2, x^12 + 2*x^11 + 2*x^10 + 2*x^9 + 2*x^7 + 2*x^4 + x^3 + 2*x^2 + 1, x^12 + x^11 + 2*x^10 + x^9 + 2*x^8 + 2*x^7 + 2*x^6 + x^5 + x^4 + 2*x^3 + x^2 + 2, 2*x^11 + 2*x^10 + 2*x^9 + x^8 + 2*x^5 + 2*x^4 + x^3 + 2*x + 1, x^12 + 2*x^11 + 2*x^10 + 2*x^9 + 2*x^8 + x^7 + x^6 + x^5 + x^4 + x^3 + 2*x^2 + 2, 2*x^12 + 2*x^10 + x^9 + x^8 + 2*x^7 + 2*x^5 + 2*x^3 + 2*x + 1 [3]: [234, 7, 151] Quasicyclic of degree 18 Linear Code over GF(3) QuasiCyclicCode of length 234 with generating polynomials: x^12 + x^9 + x^7 + 1, x^12 + x^11 + x^6 + 2*x^5 + 2*x^4 + x^3 + x^2 + x + 2, 2*x^12 + x^10 + x^9 + x^8 + 2*x^7 + x^6 + x^5 + x^4 + x^3 + 2, x^12 + x^10 + x^9 + 2*x^7 + x^6 + 2*x^5 + 2*x^4 + 2*x^3 + x^2 + 1, 2*x^12 + x^10 + 2*x^9 + 2*x^8 + x^7 + 2*x^5 + x^4 + x^3 + 2*x + 2, 2*x^10 + 2*x^9 + 2*x^8 + x^4 + x^3 + 2*x^2 + x, x^11 + x^10 + x^9 + 2*x^8 + x^7 + x^4 + 2*x^2 + 2*x + 1, x^12 + 2*x^11 + 2*x^10 + x^8 + x^6 + x^5 + 2*x^4 + 2*x^2 + x + 1, x^11 + x^10 + 2*x^5 + 2*x^3 + x^2 + 2*x + 1, 2*x^10 + x^9 + 2*x^7 + 2*x^5 + x^2 + x, x^12 + 2*x^11 + x^10 + 2*x^9 + x^3 + 2*x, 2*x^12 + 2*x^11 + x^10 + x^9 + 2*x^8 + 2*x^7 + x^6 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 2*x + 2, 2*x^12 + x^11 + 2*x^9 + 2*x^8 + 2*x^7 + x^6 + 2*x^3 + 2*x^2 + x, 2*x^11 + x^10 + 2*x^7 + 2*x^6 + 2*x^5 + x^4 + 2*x^3 + x^2 + x + 2, x^11 + x^9 + 2*x^7 + x^6 + 2*x^5 + 2*x^3 + 2, 2*x^11 + x^10 + x^8 + x^7 + x^6 + 2*x^4 + 2*x, 2*x^11 + x^10 + 2*x^8 + x^6 + 2*x^5 + x^3 + 2, x^12 + x^11 + x^9 + 2*x^8 + x^7 + x^6 + 2*x^3 + 2*x^2 + x + 2 [4]: [236, 7, 153] Linear Code over GF(3) ConstructionX using [3] [2] and [1] [5]: [232, 7, 150] Linear Code over GF(3) Puncturing of [4] at { 100, 124, 146, 223 } [6]: [231, 7, 149] Linear Code over GF(3) Puncturing of [5] at { 232 } last modified: 2008-05-17
Lb(231,7) = 148 is found by truncation of: Lb(236,7) = 153 GW2 Ub(231,7) = 151 is found by considering shortening to: Ub(230,6) = 151 DM5
GW2: M. Grassl & G. White, New Codes from Chains of Quasi-cyclic Codes, ISIT 2005.
Notes
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