lower bound: | 118 |
upper bound: | 121 |
Construction of a linear code [168,7,118] over GF(4): [1]: [170, 7, 120] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 1, 0, 0, 0, 0, 1, w, 1, w, 0, w, 0, 0, 0, w, 1, 0, 1, 1, 1, w, 0, w^2, w, 0, w, 0, 0, 1, w^2, w^2, w^2, 1, w, 1, 0, w, w^2, 1, 0, w^2, 1, w, w, 1, w^2, 0, w^2, 0, 1, 0, 0, w^2, 1, 0, w^2, w, 0, w^2, w^2, w, 0, w, 0, w^2, w, 1, 1, 0, w^2, w, 0, 1, w, 0, w^2, w^2, 1, w^2, 0, w^2, 0, 0, w, 1, 0, 1, w, 1, w, 1, w, w^2, 1, 0, w^2, 1, w^2, 0, w^2, 0, 0, 0, 1, 0, 1, w, w^2, w, 1, 1, 0, w, 1, w^2, 1, w, 0, w, 0, 0, 1, 1, w, 0, w, 0, 1, w^2, 1, w, 1, 1, 1, w^2, 1, 1, 0, w, w, w, 0, 1, 1, w^2, w^2, 0, w^2, w^2, w, w^2, w^2, 0, w, w, w^2, 0, w, w^2, w, 0, w, 1, w^2, 1, 1, w^2 ] [ 0, 1, 0, w^2, 0, 0, 1, w^2, w^2, 0, 0, 1, w^2, 1, 0, 0, 0, w^2, w^2, w, w^2, 1, w, 1, 1, 1, 0, 1, w^2, 0, 0, 0, 0, w, w, w^2, 0, 1, w, w^2, w, 0, 0, 0, w, w^2, w^2, 0, w^2, w, 1, w, 1, w^2, w, 0, 0, 1, w, w, w, w^2, w^2, 1, 0, 1, w, w^2, 0, w, w, 0, w^2, 1, 1, w^2, 1, w^2, w^2, w, 0, 1, w^2, 1, 0, w, 0, w, 1, 1, 1, 1, 1, w, w^2, 1, w^2, 1, w^2, 0, 0, w, w, 0, 1, w^2, w, w^2, w, 0, 0, w^2, 1, 0, w^2, 1, w^2, 1, 0, 1, 1, 0, w, 1, 0, w^2, w^2, w^2, 1, 0, w, 1, w^2, w, w^2, 0, 1, w^2, w, 0, 1, 1, w^2, w, w^2, 0, 1, w, 1, 1, 0, w, 0, w^2, 1, 1, 1, w^2, 1, w, 1, w, 0, w, 1, 0, 1, 0, w, 0 ] [ 0, 0, 1, w^2, 0, 0, 1, w^2, 0, 0, w^2, 1, 0, 0, w^2, 0, 1, w, 1, 1, 0, 0, 0, w, w, 0, w, w, w^2, 0, 0, 0, 0, w^2, w^2, w, w, 1, 1, 0, 0, w, 1, 1, 0, 0, w^2, w^2, 1, 1, w^2, w, w, w^2, 1, 1, 1, w, w, 1, w, 1, w, w^2, 0, 1, 0, 0, 1, 0, w^2, 0, 1, w^2, w, w, w^2, w, 1, 0, w, w, w^2, 1, 0, w, w^2, 1, 0, 0, 1, 0, w^2, w, 0, w^2, 1, w^2, w, 0, 1, 0, 0, w, w, 0, w, 0, 1, 1, 0, 1, w^2, 1, w^2, w^2, w^2, w^2, 1, w, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, w^2, w^2, 1, 1, 1, 1, 1, w^2, w^2, w, w^2, 1, 0, 1, w^2, w^2, 1, w^2, 0, 1, w^2, w, 0, w, 0, 1, w, 1, 1, 0, 0, w^2, 1, w, 0, w, w, w^2, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 0, w, 0, w, 1, w, 1, 0, 0, 1, w, w^2, w, w, w, 1, w^2, 0, 1, w^2, 1, w^2, 0, 1, w^2, w^2, 0, w, 1, w, w^2, 1, 0, w, w^2, 0, w, w^2, 0, w^2, w, w, 1, 1, 0, w, 0, w, 0, 1, w, w, 1, 0, 1, 0, w, 0, 1, w^2, 0, w^2, 1, 1, 1, w^2, w, 1, w, w^2, 0, 0, w, 0, w^2, 0, w^2, w^2, 1, w, w^2, w, 1, w, w^2, 1, w, 1, 1, 1, w^2, 0, 1, 0, w, 0, w, w^2, w, w, 0, 0, w, w^2, 1, 1, 0, w, 1, w^2, w^2, 0, 1, w^2, 1, w, w^2, w^2, 0, 0, 0, w, w^2, w, 0, w^2, 1, 1, 1, 0, w, w, 1, 1, 1, 1, w, 1, 1, 1, w^2, w, 1, 1, w^2, 1, w^2, 1, 0, w^2, w, 1, w^2, 1, 0, w, w, 1, w, w^2, 0, w^2 ] [ 0, 0, 0, 0, 0, 1, 1, 0, w^2, 1, w^2, 1, w^2, 0, w^2, 0, 1, w^2, 0, 1, 1, w^2, 0, 1, 1, w^2, 0, 1, w, w, 0, 0, 0, 1, w^2, w^2, 0, w, 1, 1, 0, 0, w^2, w^2, 0, w, w, 1, w, 0, 1, 0, w^2, w^2, w, 1, 1, w^2, 0, w, 1, 1, w^2, 1, w^2, w^2, w, w, w, 1, 0, 0, 1, w, 0, 1, w, w^2, 0, 0, 0, 1, w, w, w, w, 1, 1, w^2, w^2, w^2, w, w^2, 1, w, 1, w^2, w, 0, 0, w, w^2, w, w^2, 0, 0, w^2, 1, w^2, w, 0, w, w^2, 0, 1, w^2, 1, w^2, w, 0, 1, 0, w^2, w, w^2, 1, 1, w^2, w, w^2, 0, w, 0, w^2, w^2, 1, 0, 0, w^2, 1, w, 1, 1, 1, 0, w, w^2, 0, w^2, w, w, w, w, 0, w, 0, w, 0, 1, w^2, 1, 1, 0, 0, w, 1, w^2, 1, 1, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, 1, 1, 1, w, w^2, 1, w^2, w, 1, 1, w^2, w^2, w, 0, w, w^2, 0, w, 0, 0, w^2, w, w^2, w^2, w^2, 1, w^2, 0, w^2, 0, 0, w^2, w, w^2, 0, 1, 0, w, 0, 1, w^2, w^2, 1, 1, w, 0, w^2, 0, 1, 1, 0, w^2, 0, w, w, 1, w, 0, 0, 1, 0, 0, 0, w, 0, 1, w^2, 1, w, 1, w^2, 1, w, 0, 1, 1, 0, 0, 0, 1, w, 1, w^2, 1, 1, w, w^2, 0, w^2, w, w^2, w, 1, 1, 1, w^2, 1, w, w, 1, 1, w, 1, 1, w^2, 0, 0, 0, 1, w^2, w, w^2, 1, 0, w, w, 1, 0, 1, w, w^2, w, w^2, w, 0, 1, 1, 0, w, w, 0, w, w, 0, 0, 1, w, w, w^2, 1, w^2, w^2, 1, 1, w^2, w^2, w^2, w, w, 1, w^2, 1, w ] [ 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, w, w, 1, w, w, w, w, w^2, w^2, w, w^2, w^2, w^2, w, w^2, w^2, w^2, w, w, w^2, w^2, w, 1, w^2, w^2, w^2, w^2, 1, w^2, w, 1, w^2, w^2, w^2, 1, w, w^2, w^2, w, 1, w^2, 1, w^2, 1, w^2, w, w^2, 1, 1, w^2, w^2, w^2, 1, w, w^2, w^2, w^2, w, w^2, w^2, 1, w^2, w^2, 1, w^2, w, w^2, w, 1, w^2, w, w^2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w^2, w^2, w^2, 1, 1, 1, w, 0, 0, 0, 0, 0, w, 1, 1, 1, w^2, 1, 1, w, 1, w, w, w, w^2, w, 1, 1, w, 1, 1, w, w, 1, 1, 1, w^2, w^2, w, 1, w, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [168, 7, 118] Linear Code over GF(2^2) Puncturing of [1] at { 169 .. 170 } last modified: 2008-08-11
Lb(168,7) = 117 is found by truncation of: Lb(169,7) = 118 DG5 Ub(168,7) = 121 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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