lower bound: | 113 |
upper bound: | 115 |
Construction of a linear code [177,7,113] over GF(3): [1]: [182, 7, 117] Quasicyclic of degree 26 Linear Code over GF(3) QuasiCyclicCode of length 182 with generating polynomials: 2*x^6 + x^5 + x^4 + x^3 + x^2 + x + 1, 2*x^5 + x^4 + 2*x^3 + x^2 + x + 1, x^5 + 2*x^4 + 2*x^3 + x^2 + 1, 2*x^6 + 2*x^5 + x^4 + x^3 + x^2 + x + 1, x^5 + 2*x^4 + 2*x^3 + x^2 + 2*x + 1, x + 1, 2*x^5 + x^4 + 2*x^3 + x^2 + 2*x + 1, x^5 + 2*x^4 + x^2 + x + 1, 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 2*x + 1, 2*x^5 + x^4 + x^3 + 2*x^2 + 1, x^4 + 2*x^3 + x^2 + 2*x + 1, x^5 + x^4 + 2*x^3 + 2*x^2 + 1, x^2 + x + 1, 2*x^4 + x^3 + x^2 + 2*x + 1, x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 1, 2*x^4 + 2*x^3 + 2*x + 1, x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1, x^4 + x^2 + 1, x^4 + 2*x^3 + x^2 + 1, x^5 + x^4 + x^3 + 2*x^2 + x + 1, x^4 + 2*x^2 + x + 1, 2*x^6 + 2*x^5 + 2*x^4 + x^3 + x^2 + x + 1, 2*x^4 + 2*x^3 + x^2 + x + 1, 2*x^5 + x^4 + 2*x^3 + 2*x^2 + x + 1, 2*x^5 + 2*x^4 + x^3 + 2*x^2 + 2*x + 1, 2*x^5 + 2*x^4 + 2*x^3 + x^2 + x + 1 [2]: [178, 7, 114] Linear Code over GF(3) Puncturing of [1] at { 22, 36, 150, 160 } [3]: [177, 7, 113] Linear Code over GF(3) Puncturing of [2] at { 178 } last modified: 2004-08-16
Lb(177,7) = 112 is found by truncation of: Lb(182,7) = 117 GO Ub(177,7) = 115 follows by a one-step Griesmer bound from: Ub(61,6) = 38 follows by a one-step Griesmer bound from: Ub(22,5) = 12 is found by considering shortening to: Ub(21,4) = 12 HN
HN: R. Hill & D.E. Newton, Optimal ternary linear codes, Des. Codes Cryptogr. 2 (1992), 137-157.
Notes
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