lower bound: | 88 |
upper bound: | 91 |
Construction of a linear code [128,8,88] over GF(4): [1]: [128, 8, 88] 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, 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 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, w^2, 0, 0, w, 0, 1, 0, 0, w, w^2, w, w, w, w^2, w^2, w^2, 0, 1, 1, 0, w^2, w^2, 1, w, 1, 1, 0, w, w^2, 0, w^2, w, 1, w, 0, 1, 1, w^2, w, 0, w^2, w, 1, w, w^2, w, 0, 1, w^2, 0, w, w, w^2, 1, w^2, w, w, w^2, 1, 0, 1, 1, 1, w^2, w^2, w, w, w^2, 1, 0, w, 0, 0, w^2, w^2, 1, w, w, 0, w^2, w^2, w^2, w, 0, w, 1, 0, w, 1, w^2, w, 0, 0, 0, 1, w^2, w^2, 1, w^2, 0, w, w, 0, w^2, 1, w^2, 1, 1, 0, 1, 1, 0, 1, 0, 0 ] [ 0, 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, 0, 1, 0, 0, 0, 0, 1, 0, w^2, 0, 0, w^2, w, 0, 0, 1, 1, w, 1, w^2, 1, w, w, w, 1, w^2, 1, w^2, 1, w, 1, w^2, w^2, w, 0, w, 1, w, 0, w^2, w, 1, 0, 1, w, w^2, 0, 1, w^2, 0, w^2, 0, w, 0, 1, 0, 0, w, 1, w^2, 1, w, w^2, w, 0, 1, 0, 0, w, w^2, 0, 0, w^2, 1, w^2, w, w, w^2, 0, w^2, w^2, 1, w, 0, w, 1, w^2, w, 0, 1, w, 1, w, 0, w, 1, w, 1, 0, w, 1, 0, 1, w, 1, w^2, 0, w, w, 0, 0, 0, 1, w^2, w^2, 1, w, w^2, 0, 1, w, 0, 0, 0, w, w ] [ 0, 0, 0, 0, 1, 0, 0, 0, w^2, 0, w, 0, 1, w, 0, 0, 0, w^2, w^2, w, w^2, w^2, 1, w^2, w^2, 1, w, 1, w, w, w, w^2, 1, 1, 1, w^2, w, 1, w^2, 0, w, 0, w^2, w^2, w, 0, 0, 1, w^2, w^2, 0, 1, 0, w^2, 1, w^2, w, w^2, w^2, 0, 1, w^2, 0, 1, 0, 0, w, 0, w, 1, w^2, 0, w^2, w, 1, w^2, 0, w^2, 0, w, 1, 0, w^2, 0, w, w^2, w, w^2, w^2, 1, 1, 0, w^2, 0, 1, w^2, 1, w, 1, 0, 1, 0, w^2, w^2, 1, w, w^2, w, w^2, 0, w^2, w^2, w, 0, 0, w, 0, 0, 0, 0, 1, w^2, w^2, 1, w^2, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, w, w^2, 1, w, w^2, 0, w^2, w^2, w^2, 0, 1, w^2, w, 0, w, 0, 0, 0, w^2, 0, 1, 0, w, 0, w^2, w, w, w^2, 1, 0, w, 0, 1, 0, w^2, w^2, w, 1, 0, w^2, 0, 1, w^2, w, w^2, 1, w^2, 1, 0, 0, w^2, 1, w^2, w^2, w, 0, 0, w, w^2, w, 1, 1, w^2, 1, 1, 0, 1, 1, 0, 0, w^2, 1, w^2, w, 1, 1, w, w, w, 0, 1, 1, w, w, w, w, 1, w, 0, w, w, 1, 1, 0, 0, 1, w, 1, 1, 1, 0, w, 0, w, w^2, w^2, w, w^2, 0, w, w, 1, w^2, w^2, w^2, 0, w, w^2, w, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, w^2, 1, 0, w^2, 1, 0, 1, 1, 1, w^2, 0, w^2, 1, 0, w^2, w, w^2, w^2, 1, 1, 0, 1, 1, w^2, 0, w, 0, 1, 0, 1, w^2, w^2, w^2, w, 1, w, 1, 1, 1, 1, w^2, w, w^2, w, 0, 0, 0, 1, w^2, 1, w^2, 0, 1, 1, w, 1, w, 0, 0, 0, 1, w^2, 0, w^2, w^2, w, w, 1, 0, 0, 1, 1, 0, 0, w^2, w^2, 0, w, w, 1, 0, w^2, 0, w, w, 0, 1, w, 0, 0, w^2, w^2, 1, 1, 0, w^2, w^2, w, w, w^2, w, 0, 1, w^2, w, w^2, 1, w^2, 0, w^2, w, 0, w, w, 0, 0, w, 0, w^2, w ] [ 0, 0, 0, 0, 0, 0, 0, 1, w, 0, 1, w, 0, 1, 0, 0, 0, w, 1, w, 0, 1, w, w^2, w, w, 0, 0, 1, 0, 0, w, 1, w^2, 1, 0, 0, 1, w^2, w^2, w^2, w, 0, w^2, 0, 0, 0, 0, w, w^2, w, w^2, 1, 1, 0, 1, w^2, 0, w, 1, 0, 0, w^2, 0, w^2, 1, 1, 1, 0, w, 1, w, w^2, w, w, 1, 0, 1, 0, 0, 1, 1, w, w, 1, w^2, w^2, 0, 1, w, 0, w, w, 0, 1, w, 1, 1, w, w, 0, 0, 1, w, w, w^2, w^2, w, w, 0, 1, w^2, w, w, 0, w, 1, w, w^2, 1, w^2, w^2, 1, 1, w^2, 1, w^2, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2010-11-14
Lb(128,8) = 86 is found by truncation of: Lb(130,8) = 88 is found by concatenation of [65,8,44] and [65,8,44]-codes Ub(128,8) = 91 is found by considering shortening to: Ub(127,7) = 91 is found by considering truncation to: Ub(124,7) = 88 LP
Notes
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