lower bound: | 90 |
upper bound: | 94 |
Construction of a linear code [132,8,90] over GF(4): [1]: [134, 8, 92] 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, w, w, 0, w^2, 1, w^2, 1, w, 0, w, 1, w^2, 0, w, w, 0, w^2, w^2, w^2, 0, 1, 1, 1, w^2, w, w, 0, 1, w^2, 1, w^2, 1, w, 0, w^2, 0, 0, w^2, w^2, w^2, 1, 1, 1, w^2, 1, w^2, w, w^2, w^2, 1, 0, w, w, w^2, w, w, 0, w^2, 1, 0, 0, 1, 0, w^2, w^2, w^2, w, 1, w^2, w^2, w^2, w^2, 1, 1, 0, 0, w, w^2, 0, w^2, 0, 1, w, 1, w, 0, 0, w^2, 0, w, w^2, w^2, 1, 1, w^2, 0, w^2, w^2, w^2, w, w^2, 1, w, 0, 0, w, 1, 0, 1, 1, w, 0, 0, 1, 1, w^2, 1, 0, 0, w ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, w, 0, 0, 0, 0, 0, 0, w^2, 0, w, w^2, w, w^2, w^2, 1, 0, 1, 0, w, w, 0, w^2, 1, w, 1, w, w, w, w, 1, 0, w, w^2, 1, w, 0, 0, 1, 1, w, w, w, w, 0, w, w, w^2, w, w^2, 1, w^2, w, w^2, w, 0, w, w, 0, 1, w^2, 1, w^2, 0, w, w, w, w^2, 1, w, w^2, 1, 0, w^2, 0, w, 0, w^2, 1, 1, w^2, w^2, 1, 0, w^2, 0, 0, w, 0, w^2, 1, w^2, 1, w, 0, w, w^2, 1, 0, w, w, 0, w^2, w^2, 0, 1, 1, 1, w, w^2, 1, w^2, w, 0, 1, 1, 0, 0, 0, 0, 0, w, 0, w^2, w^2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, w^2, 0, 0, 0, w, w, 0, 1, w^2, w^2, w, 0, 0, 0, w, 1, 1, 0, 0, 1, 0, 0, w, w^2, 0, w, w^2, w, w^2, 0, 0, 0, w^2, 1, w^2, w^2, 1, 1, 1, w^2, 0, w, 0, 0, w^2, 0, w, w, 1, w^2, w^2, w, w, w^2, 0, 1, w^2, 0, 1, 0, w^2, w, w^2, 0, w, 0, 1, 1, w^2, w, 0, 0, w, 0, 1, w^2, w, w^2, w^2, 0, w, w^2, w, w, w, w, w^2, 1, w, w^2, w, w^2, 1, w, w^2, 1, w, w^2, w, w, w^2, 0, w^2, 1, 1, 0, 1, w, 1, w, w^2, 0, w^2, 0, 1, w^2, w, w, 0, 1, w^2, w^2, w^2, 0, w^2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, w, 0, 1, 0, 0, 1, 0, w^2, w, 1, 1, 1, w, w, w^2, w^2, w, w^2, 1, w^2, 1, w, w^2, 1, w^2, w^2, 0, 1, w, 1, w, w, 0, w^2, 0, 1, w, 0, 0, w, w, 0, w, w^2, w, w^2, 0, w, 0, w^2, 0, 0, w, w, w, w, 0, w^2, 1, 1, 0, w^2, 1, w, w, 0, 1, 1, w^2, 1, 1, w, 0, w^2, 0, 1, w, w, w^2, 0, 0, 1, w^2, w, 1, w, w, w, 1, 1, 0, w^2, w^2, w, 0, 0, 1, w, w, 0, 0, w^2, 0, w^2, 0, 0, 1, w, w, w^2, w^2, 0, 0, 1, 0, w, 1, 1, w^2, w^2, 1, w, w, w^2, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, w^2, 1, w, w^2, 1, w^2, 0, w^2, 0, w, 1, w^2, 1, 0, w^2, 0, 1, w^2, 1, w^2, w^2, 0, w^2, w, w, w^2, w^2, 0, 0, 1, w^2, 1, 1, 1, w^2, w^2, w, 1, 0, w, w, w, 1, w, 1, 1, 1, 1, w^2, 1, w^2, 0, 1, w^2, w, 1, w^2, w, 0, w^2, 1, 1, w^2, 0, 0, w^2, w^2, w^2, 1, 1, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w^2, 1, w, 1, 1, w, w^2, 1, 1, w, w, w, w, w, w, 0, w, 1, 0, 0, 1, w^2, w, w, w, w, 1, w, w, w^2, w^2, w^2, w^2, w, 1, 1, 0, 0, w, w, 1, w^2, w, w^2, 1, w^2, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, w^2, 1, w, 1, 0, 1, w^2, 1, 0, w^2, w, 0, w^2, w^2, 1, 1, w^2, w^2, 0, w, w, w, w, w, 1, w, 1, w, w, w^2, 0, w, w, w^2, 0, w^2, 0, 0, w^2, 1, w^2, w, 0, w^2, 1, 1, 0, 0, w^2, 0, w, 0, w, 0, w, w, w^2, w, w^2, w^2, 0, 1, w, 1, w, 1, w, w, w, 0, w, 0, 0, w, 0, w, 0, 0, w, 1, w^2, w, w, 1, w^2, w^2, 0, w^2, w, 0, w, 0, w, w, 0, 0, w^2, w^2, 0, w, w^2, 0, 0, 1, 1, 1, 1, 0, w^2, 0, 1, w^2, 0, 1, w, w^2, w, 1, w^2, w, w, 0, w^2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, w, 0, 0, 0, w^2, 0, w, w, 0, 1, 0, 0, 0, w, w^2, 0, 1, w^2, w^2, w, 1, 0, w^2, 0, 0, 1, 1, 0, 0, w^2, w^2, w, w^2, 1, w^2, 1, w^2, 0, 0, w^2, 0, 0, 1, w, 1, w, w^2, 0, w^2, w^2, w, w, w, w, 0, 0, w^2, w, w, w^2, 0, w, w, 0, w^2, w^2, 0, w, w, 1, 0, 0, 0, 0, w, w^2, w^2, 1, 1, w^2, 1, w, 1, 1, 1, w^2, 1, w, 1, w^2, w, 1, 1, 1, w, w, w, 1, 0, w^2, w^2, w^2, 0, 0, w^2, w, w^2, w, w^2, w, 1, w^2, 1, 1, 0, w^2, w^2, w^2, w, w, 1, 1, w^2, w ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, w^2, 0, w, 0, 0, w, 1, w^2, w^2, 1, w, 0, w^2, 0, w^2, 1, w, 1, w, w^2, 0, w^2, 0, w^2, 0, w, w, 0, w^2, 1, 0, w^2, w, w^2, w, 1, w, w^2, w, w^2, 0, 1, 0, w^2, w, 1, 1, w, 1, w^2, 1, w^2, w^2, w^2, 1, 1, 0, 1, 1, w^2, 0, 1, 1, w, w^2, 1, 1, 0, w^2, 1, 1, w^2, w^2, 0, w, 0, w, w, w, 0, w^2, 0, w, 1, 0, 0, w, w, 1, 0, w, w, w^2, w^2, 0, w, 0, 1, 0, w^2, 1, 0, w^2, w, w^2, w^2, 1, w^2, 1, 1, 0, 1, w^2, 0, 0, w, 1, 1, w, 0, 0, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [132, 8, 90] Linear Code over GF(2^2) Puncturing of [1] at { 133 .. 134 } last modified: 2010-11-14
Lb(132,8) = 88 is found by shortening of: Lb(133,9) = 88 DaH Ub(132,8) = 94 is found by considering shortening to: Ub(131,7) = 94 is found by considering truncation to: Ub(128,7) = 91 LP
LP: Follows from the linear programming bound.
Notes
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