lower bound: | 127 |
upper bound: | 132 |
Construction of a linear code [184,8,127] over GF(4): [1]: [185, 8, 128] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 0, w, w, 1, 0, w, w, 0, 0, 0, w, w^2, 0, w^2, 1, w, w^2, 0, w^2, w^2, 1, 1, 1, 0, 0, w, w, 0, 1, 0, 0, 0, 0, w^2, 1, 0, w^2, 1, w^2, 1, w^2, 1, 0, w, w^2, 0, 1, w, w^2, 0, w, w^2, w^2, w^2, w^2, 0, 0, w, w^2, w^2, 1, w^2, w, 1, 1, w^2, 1, 0, 1, 0, w^2, w^2, w, w, w, w, w, 0, w^2, w, 0, w^2, w^2, w, w, 0, 1, w^2, 1, w^2, w, w, 0, 0, w^2, 0, 1, 0, 1, w^2, 1, 1, w^2, w, 1, 1, w^2, w^2, 1, 0, w, w^2, w^2, w^2, 0, 0, w^2, 0, w^2, w^2, 0, w, 1, 1, w, w, 1, w^2, w, 0, w^2, w^2, 0, w, w, w, 0, 1, w, w^2, w^2, w, w, w^2, 1, 0, 0, w, w, w, w, w, 1, w, 1, 0, 1, w^2, w, 0, 1, 1, 1, 0, 0, 1, w^2, w^2, w^2, 1, w^2, 1, w^2, 1, w^2, w^2, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, w^2, 0, w, w^2, 0, w^2, w^2, 0, w, 0, w^2, 1, 0, w, w^2, w^2, w, 0, w^2, w, 0, w, 1, w, 0, w^2, w, 0, 1, w, 0, w^2, 1, w^2, 0, w^2, w, 0, 1, 0, w^2, w, 0, w, w, w^2, 0, w, 0, w^2, w, w, w, w^2, 1, 1, 0, 1, 1, 1, w^2, 0, w^2, 0, w, w, w, 1, w^2, 0, w, 1, 0, 1, 0, w, 1, w, w, w, 0, w^2, w, 0, w, 0, 1, w^2, 0, w, 0, 1, 1, w^2, 1, 1, w^2, 0, w^2, w^2, 0, 0, 0, 0, w^2, 0, 0, 1, 0, w, 0, 0, w, 1, 1, 1, 0, 0, 1, w^2, w, 1, 1, w, 0, 1, w, w^2, w^2, w, 1, w^2, 0, w, w, w^2, w, 1, 0, 0, w^2, 1, 0, 1, w^2, 0, w^2, w^2, w^2, 1, 0, 0, 1, 1, 1, w, 0, w^2, 1, w, w^2, 0, 0, w^2, w^2, w^2, w^2, w^2, w, 0, w, 1, w, w^2, w, w^2, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, w, 1, 1, w^2, w, w^2, w, 1, w^2, 0, 1, 0, w^2, w, w, w^2, w, w^2, 1, 1, 1, 0, 0, 1, w^2, w^2, w^2, w^2, 1, w^2, 0, w^2, w^2, 1, 1, 1, 0, 1, 0, 1, w, 0, 1, 0, 1, 1, 0, 0, 0, w, 1, 1, 1, 0, w^2, 1, w, w^2, w, 1, 1, 0, w, w, w, w^2, 1, 0, w^2, 0, 1, 0, w^2, 0, 1, 1, 0, 0, 0, 1, w, w, 1, 1, 0, w, w, 1, w^2, w^2, w, 0, 1, 0, w, 0, 0, 0, w^2, 0, w, 0, w^2, 0, w^2, 0, 0, w^2, w, w, 0, w, 1, 0, w, 0, w^2, 1, w, 1, 1, w^2, w, w^2, w^2, 0, 1, w^2, w^2, w, w^2, 1, 1, 0, w, w^2, 1, w^2, 1, w^2, 0, 1, w^2, 1, 0, w^2, w^2, 1, w^2, 0, 1, 1, 1, w^2, 0, w^2, w, w^2, 0, w^2, w, 1, w^2, 1, w, 1, 0, w^2, 0, w, 1, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, w, 0, 1, w, 1, w^2, 0, w^2, 0, 0, 0, w, 0, w^2, w^2, w^2, 0, w, 1, w^2, w^2, 0, 0, 0, w, w^2, w^2, w, 1, 0, w, w, 0, 1, 1, 0, w, 1, 0, 0, 1, 1, w, w, 1, 1, 1, w, w, w^2, 0, 1, w^2, 0, 1, w, w^2, 1, 1, 0, 0, w^2, 1, 1, w^2, w^2, 0, w^2, w, 0, w^2, 0, w, w, w^2, 1, w, 0, w^2, 1, 1, w^2, 0, 0, w^2, 0, w, w^2, 1, 1, w^2, w, w^2, 0, w, w, w^2, 0, w, 1, w, 1, w^2, w^2, 0, w^2, 1, 0, 0, w^2, w^2, 0, w, w^2, 1, w^2, 0, 0, w^2, w, 0, w^2, w, w, w, 1, 0, 1, w^2, w, 1, 0, w, w, w^2, w, 0, w^2, w, 1, 0, w, w^2, 1, w, w^2, 1, 1, 1, w^2, w, 1, 0, 0, w^2, 1, 1, w^2, 0, 0, 1, w, 0, 0, w^2, 1, w, 1, w, w, w^2, w, 0, w, 0, 1, w, w ] [ 0, 0, 0, 0, 1, 0, 0, w^2, 0, 1, 0, 1, w, w^2, 0, w^2, w^2, 0, w, w, 0, w, 0, w, w^2, 1, 0, w^2, 1, 1, 1, 1, w^2, 0, w^2, 0, w^2, w, w^2, 0, 0, 0, 1, 1, 1, w^2, 0, w^2, 1, 0, 0, w^2, w^2, 1, 1, w^2, w^2, 1, 0, w, w^2, w, w^2, w, 1, w, 0, 0, w, 0, 1, w^2, w, 1, w^2, w, 0, w, w^2, w, w^2, w, w, 0, w, 1, w^2, 0, 0, w, w, 0, 1, w^2, w^2, w, 0, w, 0, 1, 0, w^2, w, 1, 0, 0, w, 0, 0, w^2, 0, 0, 0, 0, w^2, 0, w, 0, w^2, w, w, 0, w^2, w^2, w^2, w, 1, w, 1, 0, 1, 1, 1, 1, 0, 0, w, 0, 0, 0, w^2, w^2, 1, 1, w, w, w^2, 1, w, w^2, w, 1, 0, 1, w, w, w, w, 1, 0, 0, 1, w^2, 1, 0, 1, 1, w^2, w^2, w^2, w, w, w^2, 0, w^2, 0, 1, w^2, w, 1, w^2, 0, 1, w, w ] [ 0, 0, 0, 0, 0, 1, 0, w, 0, 1, 1, w, 1, 1, w^2, w, w, w^2, w^2, w^2, w^2, w, 1, 0, w^2, w^2, 0, w, w, 1, 0, w^2, 0, 1, w^2, w^2, 0, w, 0, 0, w, 1, 1, 1, w, w, w, 0, 0, w^2, 1, w, 1, 1, w, w, w, w^2, w^2, w, w^2, w^2, w^2, w, 0, 0, 0, 0, w^2, w, 0, 1, w, 1, 1, 0, w, w^2, 0, w^2, 1, 1, w^2, w, w, 1, w, w^2, w^2, w^2, w, w^2, w^2, 1, w^2, 1, w^2, 1, 1, 1, w, w, 1, 1, 0, w^2, 1, 0, w, w^2, w, w, 0, w, w^2, 1, 0, 1, w, w, w^2, w, w^2, 0, 1, 0, 0, w^2, w, w^2, w^2, 1, 1, w^2, 1, w^2, 0, 0, 0, w, 0, w^2, 1, w, w^2, w, w^2, w, 1, 1, 0, 1, w^2, w^2, w, 1, w^2, 1, w^2, 1, 0, 0, 1, 1, w, w, w^2, 0, w, 0, 1, w, w^2, w^2, w, w, w, 0, w^2, 0, w^2, w^2, w^2, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, w^2, w^2, w^2, w, w, w^2, 1, 0, 1, 1, w, 1, 0, w^2, 1, 0, 0, w^2, w^2, 0, 0, 0, 1, 1, w^2, w^2, 1, 1, w, 0, 1, 1, 1, w, w, w^2, 1, w, 0, w, 0, w^2, w^2, w, w, w^2, 0, 1, 0, 1, 1, 1, w, 1, 1, w, w^2, w, w^2, w^2, w, w, 0, w^2, 0, 1, w^2, 1, 0, w, w^2, w, w, w, w^2, w, w, 0, 1, 0, 1, 0, w^2, 1, w, 0, 1, w^2, 0, w^2, w^2, 0, w^2, w^2, w^2, 1, 1, 1, 1, w, 0, w^2, w, w^2, 0, w^2, 1, w^2, w, w, w, 1, 1, 1, w, 1, 1, 0, 0, w^2, w, w^2, w^2, 1, w^2, w, w, 1, w, 1, 1, w^2, 0, w, w^2, 0, w^2, w^2, 1, w, 1, 1, 1, 1, w^2, 0, w^2, w^2, 1, 1, 1, w^2, w, 1, 0, w, w, w, w, 1, 0, 0, w^2, 1, w, w^2, 0, w^2, 1, w, 1, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, w, w^2, 1, 0, 1, 1, 0, 1, w, 0, w, w^2, 1, w^2, w, 1, w^2, w, w^2, w, 1, 1, w^2, w^2, w^2, w, w^2, w^2, w^2, w, 0, w, 1, w^2, w^2, 1, 0, 0, w^2, w^2, w^2, w, w^2, 1, w^2, 1, 0, 1, w^2, w^2, 0, 1, w^2, 1, 1, w, 0, w^2, w, w^2, 1, w, w^2, w, 1, w, 1, w^2, 1, 0, w^2, 1, 0, w, 0, w^2, w^2, 0, w^2, w, 1, 0, 0, w^2, 0, 0, w, 1, w, w^2, w, w^2, w^2, 1, w, 0, w, w, 1, 0, 1, 0, 1, w, w^2, w, 1, 0, w, w, w^2, 0, w^2, 1, 1, w, w, 0, 0, 1, 0, 0, w, 0, 0, w, 1, w^2, w, 1, w, 1, 1, w^2, 1, 0, w, w, w^2, 0, w, w, 0, w^2, 1, 0, 1, w^2, w^2, w, 1, w, w, w, 1, 1, 0, 1, 0, 0, w^2, w^2, w^2, 0, 0, w^2, w^2, 1, w^2, w, 1, 1, w, w^2, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [184, 8, 127] Linear Code over GF(2^2) Puncturing of [1] at { 185 } last modified: 2009-02-02
Lb(184,8) = 125 is found by shortening of: Lb(185,9) = 125 MST Ub(184,8) = 132 is found by considering truncation to: Ub(182,8) = 130 Da1
MST: T. Maruta, M. Shinohara & M. Takenaka, Constructing linear codes from some orbits of projectivities, to appear in Discr. Math.
Notes
|