lower bound: | 111 |
upper bound: | 111 |
Construction of a linear code [171,6,111] over GF(3): [1]: [174, 6, 114] Quasicyclic of degree 29 Linear Code over GF(3) QuasiCyclicCode of length 174 with generating polynomials: 2*x^2 + 1, x^3 + x^2 + x + 1, x^4 + x^3 + x^2 + x + 1, 2*x^5 + 2*x^4 + x^3 + 2*x^2 + x + 1, 2*x^2 + x + 1, x^3 + 2*x^2 + 1, x^4 + 2*x^3 + x + 1, 2*x^4 + 2*x^3 + x^2 + 1, x^4 + x^3 + 2*x^2 + 1, 1, 2*x^4 + x^3 + 2*x^2 + x + 1, x + 1, x^4 + 2*x^3 + 2*x^2 + x + 1, x^4 + x^3 + 2*x^2 + x + 1, x^2 + 2*x + 1, x^4 + 2*x^3 + 2*x^2 + 2*x + 1, 2*x^4 + 2*x^3 + x^2 + x + 1, 2*x^4 + x^2 + 1, 2*x^3 + x^2 + 2*x + 1, x^3 + 2*x^2 + x + 1, 2*x^4 + x^3 + 2*x^2 + 1, x^4 + x^3 + x^2 + 1, 2*x^2 + 2*x + 1, x^3 + x + 1, x^3 + 2*x + 1, 2*x^5 + x^4 + x^3 + x^2 + x + 1, 2*x^3 + 2*x^2 + 2*x + 1, 2*x^4 + x^3 + x^2 + 2*x + 1, x^4 + x^3 + x^2 + 2*x + 1 [2]: [171, 6, 111] Linear Code over GF(3) Puncturing of [1] at { 172 .. 174 } last modified: 2001-12-17
Lb(171,6) = 111 is found by truncation of: Lb(174,6) = 114 Gu1 Ub(171,6) = 111 follows by a one-step Griesmer bound from: Ub(59,5) = 37 follows by a one-step Griesmer bound from: 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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