lower bound: | 151 |
upper bound: | 151 |
Construction of a linear code [204,5,151] over GF(4): [1]: [205, 5, 152] Quasicyclic of degree 41 Linear Code over GF(2^2) QuasiCyclicCode of length 205 with generating polynomials: 1, x^3 + x^2, w^2*x^3 + x^2, x^3 + x, w^2*x^3 + x, x^3 + x^2 + x, w*x^3 + x^2 + x, w*x^3 + w*x^2 + x, x^3 + w^2*x^2 + x, w*x^3 + w^2*x^2 + x, w^2*x^3 + w^2*x^2 + x, w*x^3 + x^2 + 1, w^2*x^3 + x^2 + 1, x^3 + w*x^2 + 1, w*x^3 + w*x^2 + 1, w^2*x^3 + w*x^2 + 1, x^3 + w^2*x^2 + 1, w*x^3 + x^2 + x + 1, w^2*x^3 + x^2 + x + 1, w*x^3 + w*x^2 + x + 1, x^3 + x^2 + w*x + 1, w^2*x^3 + x^2 + w*x + 1, x^3 + w*x^2 + w*x + 1, w^2*x^3 + w*x^2 + w*x + 1, w*x^3 + w^2*x^2 + w*x + 1, x^3 + x^2 + w^2*x + 1, w^2*x^3 + x^2 + w^2*x + 1, x^3 + w*x^2 + w^2*x + 1, w*x^3 + w*x^2 + w^2*x + 1, w*x^3 + w^2*x^2 + w^2*x + 1, x^4 + w*x^3 + x^2 + x + 1, x^4 + w^2*x^3 + x^2 + x + 1, x^4 + w^2*x^3 + w*x^2 + x + 1, x^4 + w^2*x^3 + w^2*x^2 + x + 1, x^4 + w*x^3 + x^2 + w*x + 1, x^4 + w^2*x^3 + w*x^2 + w*x + 1, x^4 + w*x^3 + w^2*x^2 + w*x + 1, x^4 + w*x^3 + x^2 + w^2*x + 1, x^4 + w^2*x^3 + x^2 + w^2*x + 1, x^4 + w*x^3 + w*x^2 + w^2*x + 1, x^4 + w^2*x^3 + w*x^2 + x + w [2]: [204, 5, 151] Linear Code over GF(2^2) Puncturing of [1] at { 205 } last modified: 2001-12-17
Lb(204,5) = 151 is found by truncation of: Lb(205,5) = 152 Bo1 Ub(204,5) = 151 follows by a one-step Griesmer bound from: Ub(52,4) = 37 is found by considering truncation to: Ub(51,4) = 36 LMH
LMH: I. Landgev, T. Maruta, R. Hill, On the nonexistence of quaternary [51,4,37] codes, Finite Fields Appl. 2 (1996) 96-110.
Notes
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