lower bound: | 124 |
upper bound: | 126 |
Construction of a linear code [172,6,124] over GF(4): [1]: [172, 6, 124] Linear Code over GF(2^2) Code found by Axel Kohnert and Johannes Zwanzger Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, w^2, w, 0, w, 1, w^2, w^2, 0, 1, w^2, 0, w, w, w^2, w, w, w, 1, w^2, w^2, 0, 1, w, 0, 1, 1, 1, w^2, 1, w, 1, 1, 0, w^2, 1, 1, 0, w, w, w, w^2, 1, 0, w^2, w, w, 0, 0, 0, w, w^2, 1, 0, w^2, 0, w^2, 0, 0, 1, w, 1, w, w, w, w^2, 0, 0, 1, w^2, 0, 0, w, 0, w, 0, 1, w^2, 0, w, w^2, w^2, 1, w, w, w^2, w, w^2, w^2, w, 0, 1, 0, w, w^2, 1, w, 1, 1, w^2, 1, 1, 1, w, w, w^2, w^2, w, w^2, 0, 1, w^2, 0, w, w^2, w^2, 1, 0, 1, w, w^2, w^2, 1, 1, 1, w^2, w, 0, 1, w, 1, w, 1, 1, 0, w^2, 0, w^2, w^2, w^2, w, 1, 1, 0, w, 1, 1, w^2, 0, w, w^2, w^2, 1, 1, w, 0, w, 1, w, w, 1, 1, w, w^2, 0, w^2, w, 1 ] [ 0, 1, 0, 0, 0, 1, w^2, 1, 0, w, w, w^2, 0, w^2, w^2, 0, w^2, 1, w^2, w^2, w^2, 0, w, 1, w, w, w, w^2, w^2, 1, 0, w, w^2, 0, 0, 0, w, w, 0, w, w^2, 1, 1, w, 1, w, 1, w^2, 1, w, w^2, 1, w, w, w^2, w^2, 1, w^2, w^2, w, w^2, 1, 0, w^2, w, 0, 0, w, 1, 0, 1, 0, 1, w, 0, w^2, 0, w^2, w^2, 0, 1, 1, 1, w^2, 0, w, w^2, w^2, w, 1, w^2, w^2, 0, 0, w, 1, w^2, 1, w, w, 0, w, w^2, w, 0, w, 0, w, 0, w, 1, 1, 0, 1, w^2, w^2, w, 1, 1, 1, 0, w^2, 1, w^2, 0, 1, w^2, 0, 0, 1, 1, w^2, 1, 1, 0, 1, w^2, w, 1, 0, w, w, 0, w^2, w, w^2, w, w^2, 0, w, 1, 1, 1, w^2, w^2, 0, 0, 1, 1, w, 1, 0, 0, w^2, w, w^2, 1, w^2, 1, w, 0, w ] [ 0, 0, 1, 0, 0, w, w, w, 1, 1, w^2, w, 1, w^2, 1, 0, w, 1, 1, 1, w, 0, w, w, w, 0, w, 1, 0, w, 0, 0, w, 0, w, w, 1, w^2, w^2, 0, 0, 0, w^2, w^2, 1, 0, w^2, 1, w^2, 0, w, w^2, w^2, w, w, w, 1, w^2, w^2, 0, 1, w, w, w^2, 0, w, 0, 1, w^2, 0, w^2, 1, 0, w, w, w, 1, 1, 0, 0, w^2, 0, 0, 1, 0, w^2, w^2, 1, w^2, 0, 0, w^2, 1, w^2, w, w^2, 1, w, 1, 0, 0, w, w, w, w^2, w, w, w, w^2, 1, 1, 1, w, 1, 1, w, w^2, w^2, 1, 0, 0, 0, w, 0, w^2, 1, 0, 0, 1, 1, 1, w, 0, 0, w^2, w, 1, 1, 0, w^2, 1, w^2, w, 0, w^2, 0, w, w^2, 1, 1, 1, w, 0, 0, 1, w^2, 1, 0, 0, 1, 0, w^2, 0, w^2, w, w^2, w, 0, 1, 1, w, w^2 ] [ 0, 0, 0, 1, 0, w, w, 1, 0, w, 1, 0, w, 0, 1, 0, 0, 0, 0, w^2, 1, w^2, 1, w^2, 0, 0, w^2, 0, 0, 1, 1, 1, w, w^2, w, w^2, w^2, 0, 1, w, w^2, w^2, w^2, 0, w, 0, w, w^2, 1, w^2, w^2, 1, w, w^2, 1, w^2, 0, 0, 1, w^2, 0, w, w^2, 1, w, 0, 0, 1, 1, 0, w, w, w^2, w, 1, w, 0, 0, 0, 1, 0, 1, 0, 0, w, w, 0, 1, 1, w, w, w^2, 1, w, 1, w^2, w, 1, 0, 0, w^2, 1, 1, w^2, 1, 0, 1, w, w^2, w^2, 0, w, w^2, w^2, w^2, w, 1, 0, w^2, 0, w, w, w^2, 1, w^2, w^2, 1, w, w^2, 1, w^2, 0, 0, 1, w^2, 0, w, w^2, 1, w, 0, 0, 1, 1, 0, w, w, w^2, w, 1, w, 0, w^2, 1, w, w, 1, 0, w, 0, 1, w^2, w^2, w^2, 1, w, 0, w, w, 0, w, w ] [ 0, 0, 0, 0, 1, w^2, w^2, 0, 1, w^2, 0, 1, w^2, 1, 0, 0, 0, 0, 0, 0, w, 0, w, 1, w, w, 1, 1, 1, 0, 0, 1, w, w^2, 1, 0, 0, w^2, w^2, 0, 1, 1, w, 1, w^2, 1, w, w^2, 1, 0, 0, w, 1, 1, w^2, 1, w, 1, 0, w, 1, w, w^2, 1, 1, w^2, w^2, w, w^2, w, 0, 0, w, w^2, 0, w^2, 0, 0, 0, w, w^2, w, w^2, w, 0, 0, w, 0, 0, w^2, w^2, w^2, 1, w, w, 0, 1, w, w, w, 1, w^2, 0, w, 0, 1, 1, w, w^2, 0, w^2, 1, 0, 1, 1, 0, w^2, 1, w, 1, w^2, w, w^2, 1, 0, 0, w, 1, 1, w^2, 1, w, 1, 0, w, 1, w, w^2, 1, 1, w^2, w^2, w, w^2, w, 0, 0, w, w^2, 0, w^2, 0, w^2, 1, w, w^2, 0, 1, w^2, 1, 0, w, w, w, 0, w^2, 1, w, w, 0, w, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2008-07-29
Lb(172,6) = 123 is found by truncation of: Lb(175,6) = 126 BKW Ub(172,6) = 126 follows by a one-step Griesmer bound from: Ub(45,5) = 31 Liz
Liz: P. Lizak, Optimal quaternary linear codes, Ph. D. Thesis, Univ. of Salford, Nov. 1995.
Notes
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