lower bound: | 109 |
upper bound: | 112 |
Construction of a linear code [156,7,109] over GF(4): [1]: [159, 7, 112] Linear Code over GF(2^2) Code found by Axel Kohnert and Johannes Zwanzger Construction from a stored generator matrix: [ 1, 0, 0, 1, 0, 0, 0, 0, 1, w^2, 1, w^2, 0, w^2, 0, 0, w, w, w^2, 0, 1, 1, w, 0, w, w^2, w^2, w^2, w, 1, 0, 0, w^2, 1, 0, w, w, 0, w, w^2, 0, w^2, w, w^2, w^2, w, w^2, 0, w^2, 0, 0, w, 0, 1, w^2, 0, w, 0, 0, w^2, 1, w, w, 0, w^2, 1, 0, w^2, 0, w, w, 1, w^2, w, 1, w^2, w, 1, w^2, 1, w^2, 1, 1, w, 0, 1, 0, w^2, 0, w, w^2, w, 0, 1, 1, w, 1, 1, w, 0, w^2, 1, w^2, 1, 1, w^2, w, w^2, 0, 0, 0, 0, 1, w^2, 1, 0, w, 1, 1, w, w^2, w, w, w^2, w^2, 1, w, 1, 1, w, 0, 0, 1, w, 0, 1, 0, 0, 1, 0, w, 0, 0, w^2, w^2, 1, 0, w^2, 1, w^2, w, w^2, w, 0, w^2, 1, w^2, 0, w ] [ 0, 1, 0, w, 0, 0, 1, w, w, 0, 0, 1, w, 1, 0, 0, 0, w, w, w^2, w^2, 1, 1, 1, 1, 0, 1, w, 1, w, 0, w, w^2, w^2, w, 1, w^2, w, 0, w^2, 1, w, w, 1, w, 1, w, w, 1, 1, 1, 0, 1, 0, w, 1, 0, 1, w, 0, w^2, w^2, w^2, 1, 1, w, 1, w, 1, 0, w^2, w, 0, w^2, w^2, w^2, w^2, w, w^2, 1, 0, 1, 0, 1, w^2, w, w, w, w^2, 1, 0, w^2, 1, w^2, 1, w^2, w, 0, 0, 0, 1, 1, 0, w, 0, 0, 0, 0, w^2, w, 1, 1, 1, w, w, 0, w, 1, w^2, w^2, w, 1, 1, 0, w, 1, 0, w^2, 1, w, 1, 1, w, w^2, 0, w, w^2, w, w, w, 0, w, 0, w, w^2, 0, 0, w, w^2, 0, 0, w^2, 1, 1, 1, 1, 1, 1, 1 ] [ 0, 0, 1, w, 0, 0, 1, w, 0, 0, w, 1, 0, 0, w, 0, w, w^2, w, w, w^2, 0, w^2, w, 0, 1, 0, w^2, 1, 1, 0, 1, w^2, 1, 1, w, 0, w, w, 0, w, w, w, 0, w^2, w^2, 1, 1, 1, w, w, 1, 0, 1, 1, w, 0, w^2, 0, 1, 1, w, w, 0, w, w^2, 1, 1, w, 1, w, 0, 0, w^2, 0, 0, 1, 0, 1, 1, w, 0, 1, 0, 0, 0, 0, w^2, 1, 1, w^2, w, w, w, 0, 1, w^2, 1, w, 0, 1, w^2, 0, 0, w^2, 1, 0, 0, 0, 1, w, w, 1, 0, w, w^2, w^2, w^2, 0, w^2, w^2, 1, w^2, w^2, w, w^2, w^2, w^2, 1, 1, 0, 0, w^2, 1, w^2, 0, 1, w, w, w^2, w^2, w^2, 1, 0, 0, 1, 0, w, 1, 1, 0, w, w^2, 1, w, 0, w, 1, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 0, w^2, 0, w^2, 1, w^2, 1, 0, w, w, w^2, w, w^2, w^2, 0, w, 0, 1, 1, 1, 0, w^2, 0, w, w, w^2, 1, 0, w^2, w, w^2, 1, w^2, 1, w, w^2, 0, w, w^2, 1, 0, w, 0, 1, w^2, w^2, w^2, w, w^2, 0, w^2, 0, 1, w, 0, w, 1, w, w^2, w^2, 0, 1, w, 1, w, 0, 1, w, 1, w^2, 1, w, w^2, w^2, w, 1, w, 1, w, w^2, w, 1, 0, 1, w^2, w, 1, w^2, 0, 1, 1, w^2, w, 1, 0, w, 0, w^2, 1, w, 1, 0, w^2, w, 0, 0, w^2, 1, 0, w^2, w^2, w, w, 1, 0, w, w, 0, w, 0, 1, 1, w^2, 1, 1, w, 1, 0, w^2, 0, w^2, 0, 1, w^2, 1, w^2, w, 1, 0, w, 1, 1, 0, 1, 1, w, w^2, 0, w^2, w, 1 ] [ 0, 0, 0, 0, 0, 1, 1, 0, w, 1, w, 1, w, 0, w, 0, w, 1, 0, w, w^2, w, 1, 0, w, w, w, w, w^2, 0, 0, 1, 1, 0, w, 0, w^2, w^2, w, 0, 1, w^2, 1, 0, w^2, w, w^2, w, w^2, 1, w^2, w, w^2, w, w, 0, 0, w^2, 0, w^2, w, 1, w^2, w, 0, w^2, w, w, w, w^2, 0, w^2, 0, w^2, w, w, 1, 0, 1, w, w^2, w, w^2, w^2, 0, w^2, 1, 0, 1, w, 0, w, 0, w^2, 0, w, 1, 0, 0, w, 0, w^2, w, 0, w^2, 0, w, 1, w, w^2, 0, 1, 0, 0, w^2, w^2, w, 1, 0, 1, 1, w, 0, w, 1, w^2, w, 0, 1, 1, w^2, 1, 0, w^2, w^2, w, 0, 0, w^2, 0, 1, w^2, 1, w^2, w^2, 0, 1, 0, w^2, w, w^2, w, 0, w^2, w, 1, w, w^2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, 1, 1, 1, 1, w^2, w^2, w, w, w^2, 1, w, 1, w, 0, 1, w^2, 1, w^2, 0, w, 0, w, 0, w^2, 0, 1, 1, w^2, w^2, w, 0, 0, w^2, 1, 1, w, 1, w^2, w, 1, 0, 0, 0, 0, 0, 1, 0, 0, w^2, w^2, 1, 1, w^2, 1, 1, w, 0, 1, w, 1, w^2, w^2, 0, 0, 1, 0, 0, 1, w^2, w^2, w^2, w^2, 0, 0, w^2, w^2, w, w^2, 0, w^2, 0, 1, 0, w^2, 0, w, w, 1, 0, 1, 1, 1, w, 1, w^2, w^2, w, 1, 1, w, w, w, w^2, w^2, 1, w, 1, 1, 1, w, w^2, w, 1, 1, w^2, w, w, w^2, w^2, 1, 1, w^2, w^2, w, 1, w^2, w^2, w^2, w, w, 1, w^2, 1, w^2, w, 1, w^2, 0, w, 0, w^2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, w^2, w^2, w^2, w^2, 1, w, 1, w, w, w^2, w^2, 1, w^2, w, 1, w^2, w, w^2, w^2, 1, w, w^2, w^2, 1, 1, 1, w^2, w^2, w, 1, 1, 1, w, w, w, 1, 1, w^2, w^2, 1, 1, w^2, w^2, w, 1, w^2, w, w^2, 1, w^2, w^2, w^2, w^2, w^2, w, w^2, w, w^2, w^2, w^2, w^2, 1, w, w^2, w^2, w, 1, 1, w^2, w, 1, 1, w^2, 0, 0, w, w, w^2, w, 1, 1, w^2, w, w, w^2, w^2, w^2, 1, 1, w, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 1, 1, w^2, w, 1, 1, 1, w^2, w^2, w, 1, w, 1, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [156, 7, 109] Linear Code over GF(2^2) Puncturing of [1] at { 157 .. 159 } last modified: 2009-05-05
Lb(156,7) = 108 is found by truncation of: Lb(158,7) = 110 BKW Ub(156,7) = 112 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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