lower bound: | 112 |
upper bound: | 115 |
Construction of a linear code [160,7,112] over GF(4): [1]: [160, 7, 112] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, w^2, w, 1, 0, 0, w, 0, 1, w^2, w^2, 1, 0, 0, w, 0, w, 0, 0, 0, w^2, 1, 1, w^2, 0, 0, w, 0, 0, 1, w, w, 1, 0, w^2, w, w^2, 1, 0, w^2, 1, w, 0, w^2, 0, 1, w, 0, w^2, 1, w, w, w, 1, 0, w^2, 0, w^2, 1, w^2, 0, 0, 0, 0, 1, w, 1, 1, 1, w^2, w, 0, w^2, 1, 1, 0, 1, w, 1, w^2, 1, 1, w, 0, 1, 0, 1, 1, w, w^2, w^2, w^2, 0, 1, w, 1, 0, w^2, 0, w, w, w^2, 1, w, w^2, 1, w, w^2, w^2, 0, 0, w^2, 0, 1, 0, w, 0, 1, 1, w^2, 1, w, 1, w^2, w^2, w, 1, w^2, 1, 1, w, 1, 0, w, 0, 1, w, 0, 1, 0, w, 0, 1, 0, w, w, 1, 1, w, 0, 0, w, 1, w^2, 0, 1, 1 ] [ 0, 1, 0, 0, 0, 1, w^2, 0, 0, 1, w^2, 0, w, w, w^2, 0, 0, 0, 1, 0, w, w^2, 1, 0, 0, w^2, 0, 0, w, 1, 0, 0, w^2, w, w^2, w^2, w, w, 1, w, w, 1, 0, w, 0, w, 1, 1, 0, 0, 1, w^2, w, w, 0, w^2, 1, 0, w^2, w^2, w^2, w^2, 1, w^2, w, w, 1, w, 1, 1, w^2, w^2, w^2, w^2, 1, 1, 1, 0, 1, 1, 0, 0, w^2, 0, w^2, 0, 0, w^2, 0, 0, 1, w^2, 1, 0, 1, w, 0, w^2, w, w^2, 0, 1, w^2, 1, 0, w^2, 0, 0, w, 1, 0, w, 1, w, w, 1, w^2, 1, w^2, w, w^2, w^2, 0, w, 0, 0, 0, w, 0, 0, w^2, w^2, w, w, w^2, w^2, 0, 0, w, w, 1, 1, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 1, 0, 1, 0, w^2, w^2, w, w, w, 1 ] [ 0, 0, 1, 0, w^2, 0, 1, 0, 0, 0, 0, 0, 0, w^2, 1, 1, w^2, 0, 0, w, 0, 1, w, 0, 1, 0, w^2, w, w^2, w, 0, 0, w, w, 0, w, w^2, 1, w^2, 1, 0, w, 1, w^2, w, 0, w, 0, 1, w^2, 1, w^2, w, 0, 1, w^2, w, 0, 1, w^2, 0, w, w^2, 1, 1, 0, w^2, w^2, 0, 1, w^2, 1, w, w, w^2, 0, w^2, 1, 1, w^2, 0, 0, 1, w, w, 1, 0, w, w, 0, 0, w^2, w^2, w, w^2, w, 1, 0, w, w, 1, 0, w^2, 0, w, w, w^2, 0, w^2, 1, w^2, 0, 1, 1, w^2, w, w^2, w, 1, 0, w, 1, w, 1, 0, 1, w^2, w^2, w, 1, w^2, 1, 0, w^2, w, w^2, 0, w, 0, w^2, w^2, w, w, 0, w^2, w, w, 0, w^2, 0, w, 0, w^2, w, w^2, 0, 1, w^2, 0, 1 ] [ 0, 0, 0, 1, w, 1, 0, 0, 0, 0, 0, 0, 0, w, 0, 0, w, 1, 1, 0, w, w^2, 0, w, w^2, w^2, 0, 1, 0, 1, w^2, 0, w, w, 1, w^2, w, 0, w^2, 1, 0, w, 0, w, w^2, 1, 0, w, w^2, 1, w, 0, 1, w^2, w, 0, 1, w^2, w, 0, w^2, 1, w^2, 1, 0, 1, w, w, 1, 1, w^2, 1, w, w, w^2, 1, w, 0, 0, w, 1, w, w^2, 0, 0, w^2, w, 1, 1, w^2, w^2, 0, 0, w, w^2, w, 0, 1, w^2, w^2, 0, 0, w^2, 0, w, w, w^2, 1, w, 0, w, 1, 0, w^2, 1, 0, 1, 0, w^2, w^2, 1, w, 1, w, w^2, 1, w^2, w, w^2, 0, w, 0, 0, w^2, w, w^2, 0, w, 1, w, w, w^2, w^2, 1, 1, 0, 0, w, 1, w, 1, w^2, 0, 1, 0, w^2, 0, w, 1, w ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, w^2, w^2, 0, 0, w^2, w^2, 0, 1, 1, 1, 0, w^2, 1, 0, w^2, w^2, 0, 1, 0, 1, w^2, 0, 1, 0, 1, w^2, w^2, 1, 1, 0, 1, 0, 1, 1, w, w, 0, w, w, 0, w^2, w, 1, w^2, w^2, w^2, 0, w, w^2, 1, 0, w^2, 0, 0, w^2, w, 0, w^2, 0, w, w, w, w, w, w, w, w, 0, 1, 1, 0, w, w^2, 1, w^2, w, 1, 0, w, w, w^2, 0, w^2, w, 1, 0, w, w^2, 0, 1, w^2, 0, w^2, 0, w, 0, 1, w^2, 0, 1, w^2, w^2, w, w^2, 0, 1, 1, w, 1, w, 0, w^2, 1, w, w, w^2, 0, w^2, w^2, w, w^2, 0, w^2, w, 1, w^2, 0, w^2, 1, 0, w, 0, 0, w^2, 0, w, 1, w, w^2, w, w^2, 1, 1, w, 1, 0, w, 0, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, w, w, 1, 1, w, w, 1, 0, 0, 0, 1, w, 0, 1, w, w, 1, 0, 1, 0, w, 0, 1, 0, 1, w^2, w^2, 1, 0, 1, 0, 1, 0, 0, w^2, w^2, 1, w^2, w^2, 1, w, w^2, 0, w, w, w, 1, w^2, w, 0, 1, w, 0, 0, w^2, w, 0, w^2, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 1, 0, 0, 1, w^2, w, 0, w, w^2, 0, 1, w^2, w^2, w, 1, w, w, 1, 0, w, w^2, 0, 1, w^2, 1, w, 1, w^2, 1, 0, w, 1, 0, w, w, w^2, w, 1, 0, 0, w^2, 0, w^2, 1, w, 0, w^2, w^2, w^2, 0, w^2, w^2, w, w^2, 0, w, w^2, 0, w, 1, w, 0, 1, w^2, 1, 1, w, 1, w^2, 0, w^2, w, w^2, w, 0, 0, w^2, 0, 1, w, 0, w^2, w^2 ] [ 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, 0, 1, w, 1, w^2, w^2, w^2, w^2, w, w, w, w, 1, 1, 1, 1, w^2, w^2, w^2, w^2, 1, w, w^2, w^2, w, 1, 1, w, w^2, w^2, 1, w, w^2, w, 1, w^2, w, 1, w, 1, w^2, w, w, w^2, 1, w, w, w^2, 1, 1, w^2, w^2, w, 1, w, w^2, 1, w^2, 1, 1, w, w^2, w, w^2, w^2, w^2, w^2, w^2, w, 1, w, w, w, 1, 1, w^2, w^2, w, w, 1, 1, w^2, w^2, 1, w^2, w^2, 1, w, w, 1, 1, w^2, w, w, w^2, w^2, w^2, w, 1, 1, w^2, w^2, 1, 1, w, w, w^2, w^2, 1, 1, w, w, w^2, w^2, w, w, w^2, w^2, 1, 1, w, w^2, w, w^2, 1, 1, w^2, 0, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2007-08-03
Lb(160,7) = 111 is found by truncation of: Lb(161,7) = 112 BKW Ub(160,7) = 115 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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