lower bound: | 115 |
upper bound: | 118 |
Construction of a linear code [164,7,115] over GF(4): [1]: [165, 7, 116] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, w, w, 1, 1, 1, 1, w, w^2, 1, w^2, w^2, w^2, w^2, 1, w, 1, 1, w^2, w^2, 1, 1, w^2, w, 1, w, 1, 1, w^2, w, w, w^2, w, w^2, w^2, w^2, 1, 1, 1, w^2, 1, w^2, w, 1, w, w, w, 1, 1, w, w, 1, w^2, w, w, w, w, w^2, w^2, 0, 1, w, w, 1, w^2, w^2, w, w^2, w^2, w^2, w, w, 1, w^2, 1, w^2, 1, w^2, 1, 1, 1, w^2, w^2, w, 1, 1, w^2, w, 1, w^2, w, w^2, 0, 0, 0, 0, 0, w^2, w, w^2, w^2, w, 1, w^2, w^2, w, w^2, w^2, 1, 1, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, w, w, 1, w^2, 1, w^2, w, w^2, 1, w, 1, 1, 1, 0, 0, 0, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 1, w, 1, w, w, 0, w^2, w, 1, 1, 1, 1, 1, w^2, 0, 1, 0, 1, w, 1, w, w, w, w^2, 1, 0, 1, w^2, w, 0, 0, w^2, w, 1, 1, w, 1, 0, 1, w^2, w^2, 0, 0, 1, w^2, 0, 0, w, 0, w^2, 0, w^2, 1, w, 0, 1, w^2, 0, w, w, 0, w, w^2, 1, 1, 1, 1, w^2, 0, 0, 0, 0, 0, w, w, w^2, w, w, w^2, w^2, 0, w^2, w, w^2, 1, w^2, 0, 1, 0, w, w^2, w, 1, w, 1, w^2, w, 1, 0, 1, 0, 0, w, w^2, 0, w^2, 1, 0, 1, w, 0, w, 0, 0, 1, w^2, w^2, w, 0, 1, 0, w, 0, w^2, 0, 1, w, 0, w, w^2, w, w, w, w^2, w, 1, w, 1, 0, w, w, 0, 0, 1, 1, 1, w^2, w^2, w, w, 1, 0, w, 1, 0, 1, 0, w ] [ 0, 0, 1, 0, 0, 0, 0, w^2, w^2, 1, w^2, 0, 1, w, 1, 1, w^2, 0, 1, 0, w^2, 1, w, w, 0, 1, 0, 0, 0, w^2, w, w^2, w, w, w^2, w^2, 1, w, w^2, w, w^2, w^2, w, 1, 1, 1, 0, 0, w, 0, w^2, 0, 1, w, w^2, w, 0, w^2, w^2, w^2, 0, w^2, w, 1, w^2, w^2, 1, w, w^2, w, 1, w^2, 1, w, 1, w^2, 0, 0, 0, 0, w, w^2, 1, 1, 0, w^2, 1, 0, w, 0, 0, 0, w^2, w, 0, 1, 1, 1, w^2, w, w^2, w^2, w^2, w^2, 1, w, w, w^2, 1, 1, 0, w, 0, w^2, w, 0, w^2, w, w^2, 0, 0, 0, w, w^2, 0, 1, 1, 1, 0, w, 0, 0, w^2, 1, 0, 1, 1, 1, w, 0, 1, 0, w^2, 0, 1, w, w, 1, w, 1, w, w^2, 1, w^2, w^2, w, w^2, 1, w^2, 1, 0, 0, 1, w^2, w^2 ] [ 0, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, w^2, w^2, w, w^2, 0, w, w^2, 0, w^2, w^2, 0, w^2, 1, 1, w, w^2, w, w, 0, w, 1, 0, 1, 1, 1, 1, 1, 0, 0, w^2, 1, 1, w^2, w^2, w^2, w, w, 1, 1, 1, 1, 0, w^2, 1, w^2, w, 1, 0, w^2, 0, 0, w, w, 0, w^2, 1, w, w^2, w, w, 1, 0, w^2, w^2, w, 0, 0, 0, 0, w^2, 0, 0, w^2, 0, w^2, w^2, 1, 1, w, w^2, 1, w^2, w, w, 0, 1, w, 1, 1, w^2, w^2, 0, w^2, w, 1, w, w^2, 0, w, w^2, w^2, w^2, 0, w^2, w, w, w^2, 0, w, w^2, 0, 1, w^2, 0, w, w, w, w^2, w, 1, w, w, 0, w^2, 0, 0, w^2, w, w^2, 0, 0, 0, 0, 1, 1, 1, w, 0, 1, 1, w^2, w, w, w, 0, 1, 0, w, w, 1, 0, w^2, 1, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, w, 1, w, 1, w, 0, w^2, 0, 1, w^2, 1, w, w, 1, 0, 1, w, 0, 1, w, w^2, 0, w, 1, w^2, w, 1, w, 1, 0, w^2, w^2, 1, 1, w, 0, w, w^2, 0, 1, w, 1, 1, 1, 0, 1, w, w, 0, 1, w^2, w, 1, 0, 0, w^2, 0, 1, 1, 0, w, 0, 1, 1, 0, 1, w^2, 0, 0, w, w, w, w, w, 1, 0, w^2, 1, 0, 1, w, 1, w, 1, 0, w^2, w, 0, w^2, 0, w^2, 1, 0, 1, 0, 1, w, 0, 1, 0, 0, 1, 1, w, w^2, w^2, w^2, w, w^2, 0, 1, 0, 0, w, 1, 1, 1, w^2, w^2, 1, w, 0, 0, 0, 1, 0, 1, 0, w, w^2, w, w, 0, w, 0, 1, w, 1, 0, 1, w, w, w^2, 0, 1, w^2, w, w^2, w^2, w^2, w^2, 1, 0, w, 1, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, w^2, 0, w, w^2, 1, w, w, w^2, 0, 0, 1, 0, 1, 1, 1, w, w, 1, w, 0, 1, 0, w^2, 0, w^2, 0, w^2, w^2, 1, w^2, w, w, 1, 0, w^2, w^2, 1, w^2, 1, w, 1, 0, 0, w^2, w, 1, w^2, 0, 0, 1, w^2, w, w, 1, w, w^2, 1, w^2, w, 1, 0, w, 0, 0, 0, w^2, w^2, w^2, w^2, w, w^2, 1, 1, w, w^2, 0, 1, 0, 1, w^2, 0, w, w^2, w^2, w, 1, 1, w, w, 0, 0, w, w, 0, 1, w, w, w, w^2, 1, w^2, 0, w, w, 0, 0, 1, w^2, w, 1, w, 1, w, 0, w, 0, w^2, w, 1, 1, w, 0, 0, w^2, w^2, w, 0, w, 0, 0, w^2, 0, 0, 0, w^2, w^2, 0, 0, w^2, w^2, 1, w^2, 0, 1, w^2, w^2, 0, w, w, w^2, 1, 1, 0, w^2 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 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, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [164, 7, 115] Linear Code over GF(2^2) Puncturing of [1] at { 165 } last modified: 2008-08-11
Lb(164,7) = 113 is found by truncation of: Lb(169,7) = 118 DG5 Ub(164,7) = 118 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
|