lower bound: | 100 |
upper bound: | 103 |
Construction of a linear code [144,7,100] over GF(4): [1]: [1, 1, 1] Cyclic Linear Code over GF(2^2) RepetitionCode of length 1 [2]: [143, 6, 100] Quasicyclic of degree 11 Linear Code over GF(2^2) QuasiCyclicCode of length 143 with generating polynomials: w^2*x^12 + w*x^11 + w^2*x^10 + w^2*x^9 + w*x^8 + w^2*x^7 + x^6 + 1, x^12 + w^2*x^11 + w*x^10 + w^2*x^8 + w^2*x^7 + x^6 + w^2*x^4 + w*x^3 + x + 1, w^2*x^12 + w*x^11 + w*x^10 + w^2*x^9 + x^8 + w^2*x^6 + w^2*x^5 + w*x^4 + x + w, w*x^12 + w*x^11 + w*x^10 + w*x^9 + w^2*x^8 + w*x^5 + w*x^4 + x^3 + w^2*x^2 + x, w*x^12 + x^11 + w*x^10 + w^2*x^9 + x^8 + w^2*x^7 + w*x^6 + w^2*x^5 + w^2*x^4 + x^3 + x^2 + w, w*x^12 + w^2*x^10 + w*x^8 + w^2*x^7 + x^5 + x^4 + w*x^3 + w^2*x^2 + w^2*x + w, x^12 + w*x^11 + w*x^10 + w*x^9 + x^7 + w^2*x^5 + w^2*x^4 + w*x^2 + x + 1, w*x^12 + w^2*x^11 + w*x^10 + w*x^9 + x^8 + w*x^7 + w*x^6 + x^5 + w^2*x^4 + w*x^2 + w^2*x + w^2, w^2*x^11 + w*x^10 + w*x^8 + x^7 + x^6 + w*x^5 + x^4 + w*x^2 + x + w^2, w^2*x^11 + w*x^10 + x^9 + x^8 + w*x^7 + x^6 + w^2*x^5 + x^2 + w*x + w, w^2*x^12 + w^2*x^11 + w^2*x^10 + w*x^9 + w^2*x^8 + w^2*x^7 + w^2*x^4 + w*x^3 + w*x + w [3]: [143, 7, 99] Quasicyclic of degree 11 Linear Code over GF(2^2) QuasiCyclicCode of length 143 with generating polynomials: x^12 + w^2*x^11 + w^2*x^10 + w^2*x^7 + w^2*x^4 + w^2*x^3 + x^2, x^12 + w*x^11 + x^8 + w*x^7 + w^2*x^6 + x^4 + w^2*x^3, x^12 + x^11 + w^2*x^10 + w^2*x^9 + x^8 + w*x^6 + x^5 + w^2*x^4 + w*x^2, x^12 + w*x^10 + x^9 + x^8 + w*x^7 + w^2*x^6 + w^2*x^4 + x^2 + w^2*x, x^12 + x^11 + x^10 + w*x^9 + w*x^8 + x^7 + w^2*x^6 + w*x^5 + w*x^4 + w*x^3 + w*x^2, x^12 + w^2*x^11 + w^2*x^10 + w^2*x^9 + w^2*x^7 + x^6 + w^2*x^5 + w^2*x^4 + w*x^3 + w^2*x^2 + w*x, x^12 + w*x^11 + w^2*x^10 + w*x^9 + w^2*x^7 + x^5 + x^4 + x^2 + w^2*x, x^12 + x^11 + w*x^10 + x^9 + w^2*x^8 + w^2*x^7 + w^2*x^6 + w*x^5 + w^2*x^3 + x^2 + w^2*x, x^12 + x^11 + w*x^10 + x^9 + w^2*x^8 + w*x^6 + w*x^5 + w*x^4 + w^2*x^3, x^12 + w*x^10 + w^2*x^9 + x^8 + w^2*x^6 + w*x^5 + w*x^4 + w^2*x^3 + w^2*x^2, x^11 + x^10 + w*x^9 + x^8 + w^2*x^7 + x^6 + w*x^4 + x^3 + w^2*x^2 + w*x + 1 [4]: [144, 7, 100] Linear Code over GF(2^2) ConstructionX using [3] [2] and [1] last modified: 2002-10-19
Lb(144,7) = 100 GW2 Ub(144,7) = 103 DM3
GW2: M. Grassl & G. White, New Codes from Chains of Quasi-cyclic Codes, ISIT 2005.
Notes
|