lower bound: | 126 |
upper bound: | 129 |
Construction of a linear code [198,7,126] over GF(3): [1]: [200, 7, 128] Quasicyclic of degree 25 Linear Code over GF(3) QuasiCyclicCode of length 200 with generating polynomials: x^5 + 2*x^3 + x + 2, x^6 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + 2*x + 2, 2*x^4 + x^3 + x^2 + 2, x^6 + x^5 + 2*x^4 + 2*x^3 + x + 2, 2*x^5 + x^3 + x + 2, x^4 + x^3 + 2*x + 2, x^5 + 2*x^4 + x^2 + 2, x^4 + x^2 + 2*x + 2, 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 2, 2*x^6 + x^5 + 2*x^4 + 2*x^3 + 2*x^2 + x + 2, x^4 + 2*x^3 + 2*x^2 + 2*x + 2, 2*x^5 + x^3 + 2*x^2 + 2*x + 2, 2*x^6 + 2*x^5 + x^4 + x^3 + 2*x^2 + 2*x + 2, x^5 + 2*x^3 + 2*x^2 + 2*x + 2, x^5 + x^4 + x^3 + x + 2, x^3 + 2, 2*x^6 + 2*x^5 + x^4 + 2*x^3 + 2*x^2 + x + 2, x^6 + 2*x^4 + 2*x^3 + x^2 + x + 2, 2*x^5 + x^4 + 2*x^3 + x^2 + x + 2, 2*x^6 + x^5 + x^4 + 2*x^2 + x + 2, 2*x^6 + 2*x^5 + x^3 + x^2 + x + 2, x^6 + x^5 + 2*x^3 + x^2 + 2*x + 2, x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2, 2*x^2 + 2*x + 2, x^5 + x^4 + 2*x^2 + 2 [2]: [198, 7, 126] Linear Code over GF(3) Puncturing of [1] at { 199 .. 200 } last modified: 2001-12-17
Lb(198,7) = 126 is found by truncation of: Lb(201,7) = 129 GW2 Ub(198,7) = 129 follows by a one-step Griesmer bound from: Ub(68,6) = 43 follows by a one-step Griesmer bound from: Ub(24,5) = 14 is found by considering shortening to: Ub(23,4) = 14 is found by considering truncation 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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