lower bound: | 124 |
upper bound: | 124 |
Construction of a linear code [168,5,124] over GF(4): [1]: [172, 5, 128] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w, w, w, 0, w^2, 1, w^2, 1, w, w, w^2, w^2, 0, w, 0, 0, 0, 1, w^2, w^2, w^2, 0, w^2, 1, 1, w^2, w, w^2, w^2, w, w, 1, w, 0, 0, 0, 1, w^2, w^2, w, 0, w, w, w^2, 0, w^2, 1, 0, w^2, w^2, w, 0, w, 0, w, w^2, w^2, w^2, w, 1, 0, 0, w, 1, 0, w^2, w^2, w^2, w, w, w^2, w, 0, 1, w, w^2, 1, 0, 1, w, w, w, w^2, w^2, 1, w^2, w, 0, 0, w, 0, 0, 0, 0, w, 1, w, 1, w^2, w^2, w, w, 1, w^2, w, 1, w, 0, 0, w^2, 1, 1, 1, w^2, 0, 0, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w, w, 0, 1, 0, 0, 1, 1, 0, 1, w, w^2, w, w^2, w, w, w^2, 0, w^2, 0, 1, 1, w^2, 1, 0, w, w, w, w^2, w^2, 1, 0, w, 1, 0, w^2, w, w, 0, w, 1, w^2 ] [ 0, 1, 0, 0, 0, 0, w, w, w, w, w, w^2, w, w^2, 1, 1, 0, 1, w, w, 1, 0, 1, 0, 1, w^2, w, 0, 1, w^2, 1, w^2, 1, w, 0, w^2, 1, w, 1, w^2, w, w, w^2, 1, 1, 0, 0, w^2, w^2, w^2, 1, w, 0, 1, w^2, 0, w, w, 1, 1, w^2, w^2, 1, 0, 1, w, 0, 1, w^2, w^2, w^2, w^2, 0, 1, 1, 0, 0, 0, w, w, w, w^2, w^2, 1, 0, 0, w^2, 1, w^2, 0, w, 1, w, 0, w^2, w^2, w, w, 1, 0, w, 1, w^2, 1, w^2, w^2, w, 0, 0, 0, 1, 1, 1, w^2, w, 0, w, w^2, w^2, 1, w, w, 0, 0, 0, 1, 0, w^2, w, 1, w, w^2, 1, w, w, w^2, 0, 1, 1, 0, 0, w, w, w^2, w^2, w, 0, 0, w^2, 0, 0, 1, w, w, w^2, w, 1, 0, 0, 1, w^2, w, 0, w, 1, 0, 1, 1, w^2, w^2, w, w ] [ 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, w^2, 1, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 0, w^2, w^2, 0, 1, 0, w^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, w, 0, w, w, 0, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, 1, w, w, 1, w, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 0, 0, w^2, 0, w^2, w^2, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 0, 1, w^2, w^2, 1, w^2, w^2, 1, w^2, 1, 1, w^2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, w, 1, w, 1, 1, 1, w, w, w, 1, w, 1, w, w, w, w, w, w, w, w, w, w, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 1, 1, 0, 1, 1, 0, w, w, w, 1, 1, 0, 1, 1, 0, 0, w, 0, w, w^2, 0, w^2, 1, w^2, 1, w^2, w^2, 1, 1, w, 0, w, 0, w, w, 0, 0, w^2, 1, 1, w^2, 1, 1, w^2, w, w, w^2, w, w, w, w, w^2, 0, w^2, 1, 0, w, w, 0, 1, 0, w, 0, 0, 1, 1, w^2, w, 1, w^2, w, w^2, w, w, w^2, w^2, w, 1, 1, 0, 0, w, 0, 0, 1, w, 1, 1, 0, w^2, w, 1, w^2, 0, 1, w^2, w, w, w, w^2, w^2, w, w, w, 1, w^2, 1, 1, 0, w^2, 1, 0, w^2, 1, 0, w, 0, w, w^2, 0, w, w^2, w, w, 0, 1, w, 0, 1, 1, w^2, w, w^2, 1, 1, 1, 1, 0, 1, w^2, 0, 1, 0, 1, w^2, w, 0, w, 0, w, 0, 0, w, 0, 1, 0, 1, 1, 1, w, w^2, 1, w, w, w^2, w, 0, w, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, w^2, w^2, 1, w^2, 1, w^2, w^2, w^2, 0, 0, w^2, 0, 0, w^2, 0, 0, 0, 0, w^2, 0, w^2, 0, 0, 0, w^2, w, w^2, w^2, w, w, w, w, w^2, w^2, 1, w^2, w, w, w, 1, w, w^2, w, w, w, w, w, w, w, w^2, w, w, w^2, w, 0, w^2, w, w^2, w, w^2, w^2, w, 0, w, w^2, w^2, w, w, w^2, w^2, 0, w^2, 0, w, 0, w^2, w^2, w^2, 0, 0, 0, w, w^2, 0, 0, w^2, 0, 0, w^2, 0, w^2, w, 0, w^2, w, w^2, w, w^2, w^2, 1, w^2, w^2, w^2, 1, 1, 1, w^2, w, 1, 1, w^2, 1, 1, 1, 1, 1, w, 1, w^2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, w^2, w^2, w^2, 0, 0, 1, 0, 0, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [168, 5, 124] Linear Code over GF(2^2) Puncturing of [1] at { 169 .. 172 } last modified: 2001-12-17
Lb(168,5) = 124 is found by truncation of: Lb(172,5) = 128 Liz Ub(168,5) = 124 follows by a one-step Griesmer bound from: Ub(43,4) = 31 follows by a one-step Griesmer bound from: Ub(11,3) = 7 is found by considering truncation to: Ub(10,3) = 6 GH
Liz: P. Lizak, Optimal quaternary linear codes, Ph. D. Thesis, Univ. of Salford, Nov. 1995.
Notes
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