lower bound: | 144 |
upper bound: | 145 |
Construction of a linear code [222,7,144] over GF(3): [1]: [1, 1, 1] Cyclic Linear Code over GF(3) RepetitionCode of length 1 [2]: [221, 6, 144] Quasicyclic of degree 17 Linear Code over GF(3) QuasiCyclicCode of length 221 with generating polynomials: 2*x^11 + x^9 + 2*x^8 + x^7 + 2*x^6 + 1, x^11 + 2*x^8 + 2*x^7 + x^3 + 2*x^2 + 1, 2*x^11 + 2*x^10 + x^9 + x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x + 2, x^12 + 2*x^11 + x^9 + x^7 + 2*x^4 + 2*x^3, x^12 + x^10 + 2*x^9 + x^8 + 2*x^7 + x^6 + 2*x^4 + x^2 + 1, x^12 + x^11 + 2*x^10 + x^9 + x^8 + x^3 + 2*x^2 + 2*x + 1, x^11 + 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x^2, x^11 + 2*x^10 + x^9 + x^8 + x^7 + x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1, x^12 + x^11 + x^10 + 2*x^9 + x^8 + x^5 + 2*x^3 + 2*x^2 + x, 2*x^11 + 2*x^10 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x + 2, x^12 + x^11 + x^8 + 2*x^5 + 2*x^2 + 2, x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x + 1, x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 2*x + 2, x^11 + 2*x^10 + 2*x^7 + 2*x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 1, 2*x^11 + x^10 + 2*x^8 + x^7 + 2*x^6 + 2*x^5 + 2*x^3 + x + 2, x^11 + x^10 + 2*x^9 + 2*x^8 + 2*x^7 + 2*x^5 + 2*x^2 + x + 2, 2*x^12 + 2*x^11 + x^10 + x^8 + x^7 + x^6 + 2*x^5 + x^4 + x [3]: [221, 7, 143] Quasicyclic of degree 17 Linear Code over GF(3) QuasiCyclicCode of length 221 with generating polynomials: 2*x^11 + x^9 + 2*x^8 + x^7 + 2*x^6 + 1, 2*x^12 + 2*x^10 + 2*x^9 + x^8 + x^7 + 2*x^6 + 2*x^5 + 2*x^4 + x^2 + 2*x, x^12 + 2*x^9 + x^8 + x^7 + 2*x^6 + x^3 + 2*x^2, x^12 + 2*x^11 + x^9 + x^7 + 2*x^4 + 2*x^3, 2*x^11 + x^9 + x^7 + 2*x^5 + x^4 + 2*x^3 + 2*x, x^10 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + x^2 + x, x^12 + 2*x^11 + x^10 + x^9 + x^8 + x^7 + 2*x^4 + 2*x^3 + x + 1, x^12 + 2*x^11 + 2*x^9 + 2*x^8 + 2*x^7 + 2*x^6 + 2, x^12 + x^11 + x^10 + 2*x^9 + x^8 + x^5 + 2*x^3 + 2*x^2 + x, 2*x^11 + 2*x^10 + 2*x^9 + 2*x^7 + x^6 + x^4 + x^3 + 2*x + 2, 2*x^12 + 2*x^11 + x^10 + x^9 + 2*x^8 + x^7 + x^6 + x^4 + x^3 + x, x^12 + 2*x^11 + 2*x^10 + 2*x^9 + x^8 + 2*x^7 + 2*x^6 + 2*x + 1, x^12 + x^11 + x^10 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 2*x + 2, 2*x^12 + x^10 + 2*x^9 + 2*x^8 + x^7 + x^6 + x^4 + x^3 + x^2 + 2*x, 2*x^12 + x^11 + 2*x^9 + x^8 + x^6 + x^5 + 2*x^4 + x^3 + 2*x^2 + 1, x^12 + 2*x^11 + 2*x^10 + x^6 + x^4 + x^3 + 2*x, x^12 + x^11 + 2*x^9 + x^5 + 2*x^3 + 2*x^2 + 2 [4]: [222, 7, 144] Linear Code over GF(3) ConstructionX using [3] [2] and [1] last modified: 2003-10-08
Lb(222,7) = 144 BKW Ub(222,7) = 145 follows by a one-step Griesmer bound from: Ub(76,6) = 48 follows by a one-step Griesmer bound from: Ub(27,5) = 16 is found by considering truncation to: Ub(26,5) = 15 is found by construction B: [consider deleting the (at most) 3 coordinates of a word in the dual]
Notes
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