lower bound: | 162 |
upper bound: | 168 |
Construction of a linear code [232,8,162] over GF(4): [1]: [234, 8, 164] 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, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, w^2, 0, w, w, w, w^2, 1, 0, 0, 0, w^2, 1, w, w^2, w^2, 0, w, 1, w^2, 1, w, w^2, w^2, w^2, w, 0, w, 0, 0, w, 0, 1, w, w^2, w, w^2, 1, w^2, w^2, w, 1, w, w, 0, 0, w^2, 0, 1, 1, w^2, 0, w^2, w, 1, 0, 1, 1, 0, w^2, 1, 1, 1, 0, 0, 1, 1, 0, w, w, 1, w^2, 0, 1, w^2, w, 0, 1, w^2, 1, 0, w^2, 0, w, 0, w^2, 0, 1, w, 0, w^2, w, 1, w^2, 0, w^2, 0, 1, w, w, w^2, 1, 1, 0, w, 0, 1, w, 1, w, 1, 1, w, w^2, w^2, 1, 1, 0, w, 0, w, 1, 0, w^2, 1, w^2, w, w, w^2, w, w, w, 0, 1, 0, w, w^2, w, w, 0, 1, w, 1, 1, 0, 0, 0, 0, w, 0, w^2, 1, w, 0, 1, w, w, w^2, 0, 1, 0, w, 0, w, 0, 1, w^2, 0, w^2, 0, 1, 0, 1, 0, 0, w, 1, w, 0, w^2, w^2, w, w^2, 1, w^2, 0, w, w^2, w, 1, w^2, w, 1, 1, 1, 1, w^2, w, w^2, 0, w, w^2, 0, w, 1, 1, 1, w^2, w, 1, 1, 1, 1, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, w^2, w, 0, 0, 1, w, 1, 0, 0, w^2, w, w^2, 1, 0, w^2, w, w^2, w, w, w^2, 1, 0, 0, 1, w, w, w, 0, w, w, 1, w^2, 1, 1, 1, w, w, 0, 1, w^2, w^2, w, w, 0, w^2, w^2, 1, 0, w, w^2, w^2, 1, w^2, 1, 1, 0, 1, w^2, w, 0, 0, 1, 0, 1, 0, 1, w, 0, w^2, w, w^2, 1, w, 1, w, 1, w, w, 1, w^2, w^2, w, w, w^2, w^2, 1, w^2, w, w^2, 1, w^2, w, w^2, w^2, w^2, 1, w^2, 0, 1, w, 0, 1, w, w, w^2, w^2, w^2, w^2, w^2, 0, w^2, 1, 0, w, 0, 1, w, w, w, w^2, 1, w^2, w, w, 1, w, 1, 1, 0, 0, w, 1, 1, w, 1, 1, 0, w, 1, w^2, w^2, 0, 1, 0, 0, 0, 1, w, w^2, w, w^2, w, 1, w^2, 0, 1, w^2, 1, 1, w, w, w, w, 1, w, w^2, w^2, 1, 1, 1, 1, 1, 0, w, w^2, w^2, w, w^2, 0, 1, 1, w, w, w^2, w, 1, 1, w^2, w, 1, w^2, 0, 0, 0, w, 1, 1, w^2, w, 1, w^2, w, w^2, 0, 0, w, 1, w^2, 0, 1, 0, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, w^2, 1, w^2, w, 0, 0, 1, w, 1, 0, 0, w^2, w, w^2, 1, 0, w^2, w, w^2, w, w, w^2, 1, 0, 0, 1, w, w, w, 0, w, w, 1, w^2, 1, 1, 1, w, w, 0, 1, w^2, 1, w, w, 0, w^2, w^2, 1, 0, w, w^2, w^2, 1, w^2, 1, 1, 0, 1, w^2, w, 0, 0, w, 0, 1, 0, 1, w, 0, w^2, w, w^2, 1, w, 1, w, 1, w, w, 1, w^2, w^2, w, w, w^2, w^2, 1, w^2, w, w^2, 1, w^2, w, w^2, w^2, w^2, 1, w^2, 0, 1, w, 0, 1, w, 1, w^2, w^2, w^2, w^2, w^2, 0, w^2, 1, 0, w, 0, 1, w, w, w, w^2, 1, w^2, w, w, 0, w, 1, 1, 0, 0, w, 1, 1, w, 1, 1, 0, w, 1, w^2, w^2, 0, 1, 0, 0, w^2, 1, w, w^2, w, w^2, w, 1, w^2, 0, 1, w^2, 1, 1, w, w, w, w, 1, w, w^2, w^2, 1, 1, 1, 1, 1, 0, w, w^2, w^2, w, w^2, 0, 1, 1, w, w, w^2, w, 1, 1, 0, w, 1, w^2, 0, 0, 0, w, 1, 1, w^2, w, 1, w^2, w, w^2, 0, 0, w, 1, w^2, 1, 1, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, w^2, w^2, 1, 0, w^2, 1, 1, w, 1, w^2, 1, 1, 1, 0, 1, w, w, 1, w, 0, 0, 0, w, w, 0, w^2, w, w, 0, 0, w^2, 0, w, 1, w, 0, w, 1, 0, 1, w^2, w, 1, w, 1, 0, w, w, w, 0, 1, 1, w, 1, w, 0, 1, w^2, 0, w, w^2, 0, w, w^2, 1, 1, w, w^2, w^2, w^2, w^2, w^2, 0, w^2, w, 0, 1, 0, w, 1, 1, 1, w^2, 1, w, w, 1, 1, 0, 0, w, w, w^2, 1, w^2, w, 1, w^2, 0, 1, 0, w, w, 1, w^2, w^2, w, 1, w, w, 1, w^2, 0, 0, 1, w, w, 1, 0, w^2, w, 0, 0, 0, 0, w, w^2, 0, w^2, w^2, 0, 1, w, w^2, w, 0, w^2, 1, 1, 0, 0, w, w^2, 0, 1, 0, 1, w^2, w, w^2, 1, w, w, 0, w^2, 0, 0, 0, w^2, w^2, 1, 0, w, w^2, 1, 1, 1, 1, w, 1, 0, 1, 1, w^2, 1, 0, w^2, 0, 1, 1, w^2, 0, w, w, 0, 0, 0, 0, 0, w, w^2, 0, w, 1, w^2, w, 1, 1, w^2, 0, w, w^2, w, w^2, w, w^2, w, w^2, 0, 1, 0, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, w^2, w^2, 1, 0, w^2, 1, 1, w, 1, w^2, 1, 1, 1, 0, 1, w, w, 1, w, w^2, 0, 0, w, w, 0, w^2, w, w, 0, 0, w^2, 0, w, 1, w, 0, w, 1, 0, 1, 0, w, 1, w, 1, 0, w, w, w, 0, 1, 1, w, 1, w, 0, 1, w^2, 0, w, w^2, w^2, w, w^2, 1, 1, w, w^2, w^2, w^2, w^2, w^2, 0, w^2, w, 0, 1, 0, w, 1, 1, 1, 1, 1, w, w, 1, 1, 0, 0, w, w, w^2, 1, w^2, w, 1, w^2, 0, 1, 0, w, w, 0, w^2, w^2, w, 1, w, w, 1, w^2, 0, 0, 1, w, w, 1, 0, w^2, w, 0, 0, 0, 0, w, w^2, 0, w^2, w^2, 0, 1, w, w^2, w, 0, w^2, 1, 1, 0, 0, w, w^2, 0, 1, 1, 1, w^2, w, w^2, 1, w, w, 0, w^2, 0, 0, 0, w^2, w^2, 1, 0, w, w^2, 1, 1, 0, 1, w, 1, 0, 1, 1, w^2, 1, 0, w^2, 0, 1, 1, w^2, 0, w, w, 0, 0, 0, 0, 0, w, w^2, 0, w, 1, w^2, w, 1, 1, w^2, 0, w, w^2, w, w^2, w, w^2, w, w^2, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, w, 0, 1, w^2, w^2, 1, 0, w^2, 1, 1, w, 1, w^2, 1, 1, 1, 0, 1, w, w, 1, 1, w^2, 0, 0, w, w, 0, w^2, w, w, 0, 0, w^2, 0, w, 1, w, 0, w, 1, 0, w^2, 0, w, 1, w, 1, 0, w, w, w, 0, 1, 1, w, 1, w, 0, 1, w^2, 0, w, 1, w^2, w, w^2, 1, 1, w, w^2, w^2, w^2, w^2, w^2, 0, w^2, w, 0, 1, 0, w, 1, 1, w, 1, 1, w, w, 1, 1, 0, 0, w, w, w^2, 1, w^2, w, 1, w^2, 0, 1, 0, w, 0, 0, w^2, w^2, w, 1, w, w, 1, w^2, 0, 0, 1, w, w, 1, 0, w^2, w, 0, 0, 1, 0, w, w^2, 0, w^2, w^2, 0, 1, w, w^2, w, 0, w^2, 1, 1, 0, 0, w, w^2, 0, 1, 1, 1, w^2, w, w^2, 1, w, w, 0, w^2, 0, 0, 0, w^2, w^2, 1, 0, w, w^2, 1, 0, 0, 1, w, 1, 0, 1, 1, w^2, 1, 0, w^2, 0, 1, 1, w^2, 0, w, w, 0, 0, w^2, 0, 0, w, w^2, 0, w, 1, w^2, w, 1, 1, w^2, 0, w, w^2, w, w^2, w, w^2, w, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, w, w, w, w^2, 1, 0, 0, 0, w^2, 1, w, w^2, w^2, 0, w, 1, w^2, 1, w, w^2, 0, w^2, w, 0, w, 0, 0, w, 0, 1, w, w^2, w, w^2, 1, w^2, w^2, w, 1, w, w^2, w^2, 0, w^2, 0, 1, 1, w^2, 0, w^2, w, 1, 0, 1, 1, 0, w^2, 1, 1, 1, 0, w, 0, 1, 0, w, w, 1, w^2, 0, 1, w^2, w, 0, 1, w^2, 1, 0, w^2, 0, w, 0, 0, 1, 1, w, 0, w^2, w, 1, w^2, 0, w^2, 0, 1, w, w, w^2, 1, 1, 0, w, 0, w^2, 0, 1, w, 1, 1, w, w^2, w^2, 1, 1, 0, w, 0, w, 1, 0, w^2, 1, w^2, w, 1, w, w, w, w, 0, 1, 0, w, w^2, w, w, 0, 1, w, 1, 1, 0, 0, 0, 0, w, w^2, w^2, 1, w, 0, 1, w, w, w^2, 0, 1, 0, w, 0, w, 0, 1, w^2, 0, w^2, w, 0, 0, 1, 0, 0, w, 1, w, 0, w^2, w^2, w, w^2, 1, w^2, 0, w, w^2, w, 1, 0, 1, 1, 1, 1, 1, w^2, w, w^2, 0, w, w^2, 0, w, 1, 1, 1, w^2, w, 1, 1, w^2, w, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, w, w, w, w^2, 1, 0, 0, 0, w^2, 1, w, w^2, w^2, 0, w, 1, w^2, 1, w, w^2, w^2, w^2, w, 0, w, 0, 0, w, 0, 1, w, w^2, w, w^2, 1, w^2, w^2, w, 1, w, w^2, 0, 0, w^2, 0, 1, 1, w^2, 0, w^2, w, 1, 0, 1, 1, 0, w^2, 1, 1, 1, 0, w, 1, 1, 0, w, w, 1, w^2, 0, 1, w^2, w, 0, 1, w^2, 1, 0, w^2, 0, w, 0, 0, 0, 1, w, 0, w^2, w, 1, w^2, 0, w^2, 0, 1, w, w, w^2, 1, 1, 0, w, 0, w^2, w, 1, w, 1, 1, w, w^2, w^2, 1, 1, 0, w, 0, w, 1, 0, w^2, 1, w^2, w, 1, w^2, w, w, w, 0, 1, 0, w, w^2, w, w, 0, 1, w, 1, 1, 0, 0, 0, 0, w, 0, w^2, 1, w, 0, 1, w, w, w^2, 0, 1, 0, w, 0, w, 0, 1, w^2, 0, w^2, w, 1, 0, 1, 0, 0, w, 1, w, 0, w^2, w^2, w, w^2, 1, w^2, 0, w, w^2, w, 1, 0, w, 1, 1, 1, 1, w^2, w, w^2, 0, w, w^2, 0, w, 1, 1, 1, w^2, w, 1, 1, w^2, 1, 0, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [232, 8, 162] Linear Code over GF(2^2) Puncturing of [1] at { 233 .. 234 } last modified: 2010-02-16
Lb(232,8) = 159 is found by truncation of: Lb(233,8) = 160 MST Ub(232,8) = 168 is found by considering truncation to: Ub(229,8) = 165 DM4
MST: T. Maruta, M. Shinohara & M. Takenaka, Constructing linear codes from some orbits of projectivities, to appear in Discr. Math.
Notes
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