lower bound: | 120 |
upper bound: | 124 |
Construction of a linear code [172,7,120] over GF(4): [1]: [172, 7, 120] 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, 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, 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, 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, 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 ] [ 0, 1, 0, 0, 0, 0, 0, w^2, 0, w^2, 1, w^2, 0, 1, w, w^2, w^2, 1, w^2, w^2, 1, w, 0, 1, 0, w^2, 1, 0, w, 0, 0, 1, 0, w, 0, w^2, w, w^2, 1, w, w, w^2, 0, 0, 1, 1, 1, 0, w, w^2, 0, w, 1, 0, 0, w, 1, w, 1, 0, w, w^2, w, 0, w^2, 1, 1, 0, w, 1, w, 0, w, 1, 0, w^2, 0, 1, w, w^2, 1, w^2, 1, 1, w, w, w^2, w^2, w^2, 0, w^2, 1, w, w, 0, 0, w^2, w, w^2, 1, w^2, 0, w^2, 1, 0, w^2, w, 0, 0, 0, 1, 0, w, w^2, 1, w, 0, 1, w, 1, 1, 1, 1, 1, w^2, w^2, 1, w, w, w^2, 1, 0, 1, 1, w, 0, w^2, 0, 0, 1, 0, w, w^2, w^2, w^2, 1, w^2, 0, 0, 1, 0, 0, 0, w^2, w, w^2, 1, w^2, 1, 0, w, w^2, 1, 1, w^2, 1, 0, w^2, w, 0, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, w, w^2, 0, 1, 1, w, w, w^2, 0, 1, 0, w, 0, 1, w, w, w^2, 0, w^2, w^2, w, 0, 1, w^2, 1, 1, w^2, w^2, 0, w^2, 0, 1, 0, w^2, w^2, 0, w, 0, 0, w, w^2, w^2, 0, w, 1, 1, w, 1, 0, w^2, 1, w, w, 1, 1, w^2, w^2, w, 0, 0, 1, w, 0, w, 1, w, w^2, 0, 0, 0, w, 1, w^2, 0, 1, w^2, 1, w, w^2, 1, 0, w, w, w, 0, 1, 0, 1, w^2, 1, 1, 1, 1, w, w^2, 1, 0, 1, 0, 1, w^2, 1, 0, 1, 1, w, w, w^2, 1, 0, w^2, w, w^2, 0, w^2, 1, 0, 0, w^2, w, w^2, 1, w^2, 0, 0, w^2, w, 0, 1, 0, 1, w^2, 0, w, 1, w^2, 0, w, w^2, w, w^2, w^2, w^2, 0, 1, 0, 0, w^2, 1, 0, 1, 1, 0, 1, 0, 1, 1, w^2, w^2, w^2, w, w^2, 0, 0, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 1, w, 0, 0, w, w, w^2, 0, 1, 1, w^2, 0, 0, w, 0, 1, w^2, w, w^2, 0, 0, w, 0, w^2, w^2, 1, w^2, w, 1, w, w^2, w, 1, 0, w, w, w, w, 0, 0, w^2, w^2, 1, 0, 0, w^2, w^2, w, 1, w, 1, 1, w^2, 0, w, w^2, 0, w^2, 0, 1, w^2, 1, w^2, w^2, w^2, 1, 1, w, w^2, 1, w, w, w^2, 1, 0, 0, 0, 0, 0, 1, w^2, w^2, w, 0, w, 0, w^2, w^2, 1, w^2, w, w^2, w^2, w, 0, w^2, w^2, w^2, 0, 1, w^2, w, 0, 0, w, 1, 0, w, w^2, w^2, 1, w, 0, w^2, 1, 1, 0, w^2, w^2, w, w^2, 0, 0, 0, w, 1, w^2, w^2, w, w^2, 0, 1, w^2, 0, w, w^2, w, w^2, w, 1, 0, w, 1, w, 0, w, w^2, 0, 0, 1, 0, w^2, w^2, w, 1, w, 0, 0, w^2, w^2, w, w, 0, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, w, 0, w^2, 1, w, 0, w^2, 1, 0, w^2, 0, w^2, w, 1, w, 0, 1, w, w, w^2, 0, 1, 0, 0, 1, 0, 1, 0, w^2, w, w^2, 1, 1, 1, w, 1, w, 0, w, 0, w^2, w^2, 1, w^2, w^2, w, 1, 1, w^2, w, w^2, w, w^2, w^2, 0, 0, w^2, 0, w, w, w, 0, 0, 0, w, 0, w, w, 1, w^2, 0, w^2, 1, w, 1, w, 0, w^2, w^2, w, w^2, w, 0, w^2, w^2, w^2, w, w^2, 0, 0, w, w, 1, w^2, w, w, 1, 0, 0, 1, w, 0, 0, w, 0, 1, w, w^2, w, 1, w^2, w, w, w^2, 1, 0, 0, w, w^2, 1, 0, 0, w^2, w, w, w, 0, 1, w^2, 0, w^2, w, 1, w^2, 0, 0, w, 0, w, 0, w, w^2, 1, 1, 1, w, 1, 1, w^2, w, w, 0, w, 1, w^2, 0, 1, w, 0, 1, 1, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 1, w^2, 0, 0, w, w^2, 1, 0, 1, w, 1, 0, 0, w^2, 0, 1, 1, w, 1, 0, 1, w^2, w, 0, 1, 1, w^2, 0, 1, w, w^2, w, w, 0, w, w^2, 0, 1, 1, 1, w, 0, 0, w^2, w^2, 0, w, 1, 0, 0, 0, w^2, w, 1, 1, 0, w, w, w, w^2, w, w^2, w, w, 0, 0, w^2, 1, w, w^2, 1, 0, w, w^2, w^2, 1, w, w^2, 0, 0, w, 1, w, w, 1, 0, w^2, 1, w, w^2, w, 1, 0, w^2, 0, w^2, w, 1, w, 1, w^2, w, 1, 0, 0, w, w, w, 1, 0, 1, w^2, 0, 1, w, w, 0, w, w^2, w, 0, 1, w, w^2, w, 0, 1, 0, 1, w, w, 0, 0, 1, 1, 0, 0, w, w^2, 1, w, 1, 0, w^2, w, w, 1, w^2, 1, 1, w, 0, 1, 0, 0, w, 1, w^2, 1, w, w, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, w, w^2, 1, 0, 1, w, 1, w^2, 0, 1, 0, 1, w, w^2, 1, 1, w, 0, w, w^2, 1, 0, 1, w, 1, w^2, w, w^2, 0, w^2, 0, 1, 0, 0, w, 0, w^2, w^2, w^2, w^2, 0, 0, w, w^2, w, 0, w^2, w, w^2, 1, w, 0, w^2, w, w, 1, 1, w^2, w, w^2, 0, 0, w, w^2, w, w^2, 0, w^2, 1, w^2, 0, w, 0, 1, 0, 1, w, 0, w, 1, 0, 0, w^2, 1, 0, 1, 1, 1, 1, w^2, 0, w^2, w^2, w, 0, 1, 0, w, 0, w^2, w, w, w, 1, 0, 1, w, w, 1, 0, w^2, 1, w, w, w, 1, 1, 0, w^2, w, w, w, 0, 1, w^2, 0, 0, 1, 0, w^2, 1, 1, w, 1, 1, w, w, 1, 0, 0, w, w, 1, w^2, 1, 1, w^2, 0, w, 1, 0, 1, w, w, 1, 0, 0, 1, 0, w^2, 0, w^2, 0, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2008-03-25
Lb(172,7) = 119 AAG Ub(172,7) = 124 DM3
DM3: R. N. Daskalov & E. Metodieva, Bounds on minimum length for quaternary linear codes in dimensions six and seven, Mathematics and Education in Mathematics, Sofia, (1994) 156-161.
Notes
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