lower bound: | 42 |
upper bound: | 42 |
Construction of a linear code [66,5,42] over GF(3): [1]: [1, 1, 1] Cyclic Linear Code over GF(3) RepetitionCode of length 1 [2]: [66, 5, 42] Quasicyclic of degree 11 Linear Code over GF(3) QuasiCyclicCode of length 66 with generating polynomials: 2*x^5 + 1, 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1, x^3 + x^2 + 1, x^5 + 2*x^4 + x^3 + 2, 2*x^5 + x^3 + x^2 + 2*x, 2*x^3 + 2*x^2 + 2*x, 2*x^5 + x^3 + 2*x^2 + x, 2*x^5 + x^3 + x^2 + x + 1, x^5 + 2*x^4 + 2*x^3 + 1, 2*x^5 + x^4 + x^3 + 2*x^2 + x + 2, x^5 + 2*x^3 [3]: [66, 6, 41] Quasicyclic of degree 11 Linear Code over GF(3) QuasiCyclicCode of length 66 with generating polynomials: 1, 2*x^4 + x^3 + 2*x, x^5 + x^4 + 2*x^3 + 1, x^5 + x^3 + x^2 + x, x^3 + 2*x^2 + x + 1, x^5 + x^4 + 2*x^2 + x + 1, x^5 + x^4 + 2*x^3 + x^2 + 2*x + 2, 2*x^5 + 2*x^4 + x^2 + 2*x, 2*x^4 + x^3 + x^2 + x + 2, 2*x^5 + x^3 + x, x^5 + x^4 [4]: [67, 6, 42] Linear Code over GF(3) ConstructionX using [3] [2] and [1] [5]: [66, 5, 42] Quasicyclic of degree 11 Linear Code over GF(3) Shortening of [4] at { 67 } last modified: 2001-12-17
Lb(66,5) = 42 is found by shortening of: Lb(67,6) = 42 Ha Ub(66,5) = 42 follows by a one-step Griesmer bound from: Ub(23,4) = 14 is found by considering truncation to: Ub(21,4) = 12 HN
Ha: N. Hamada, pers. comm.
Notes
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