lower bound: | 130 |
upper bound: | 133 |
Construction of a linear code [184,7,130] over GF(4): [1]: [186, 7, 132] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 1, 0, 0, w^2, w^2, w, w^2, w, w, 1, w^2, 0, 0, w^2, w, 0, 0, w^2, 0, 1, w^2, w^2, 0, 1, w, 1, 1, w, 1, w, 1, w^2, w, w^2, 1, 1, w, 0, 0, 1, 0, 0, w^2, 1, w^2, 0, 1, 0, w^2, w, w, w, w, w^2, w^2, w^2, w, 1, 0, 0, w^2, w, w, w, 1, 0, 0, w^2, w^2, 1, w, 0, w, w, w^2, 1, 1, 0, w, 1, 0, 1, w^2, w^2, 0, 0, w, 1, w, 0, 1, 0, 1, w, w, w^2, w, w^2, w, w, 1, 0, 1, 1, w^2, w, 1, w, w, 1, 1, w^2, 1, w^2, w, w, w, w^2, 0, w^2, w^2, w^2, w, 0, w^2, w, w^2, 0, w, 0, 0, 1, w^2, w^2, 0, 0, 0, w, 1, w, 0, w, 1, 0, w^2, 1, w^2, w^2, 0, 0, 1, w, 0, w^2, 0, w^2, w, 0, w, 1, w, 1, w, 0, 1, w^2, w^2, 0, 0, w^2, 0, w, w, 0, w^2, 1, w^2, 1, w^2, 1, 1 ] [ 0, 1, 0, 0, 0, w^2, 0, 0, w, w, w, 0, w, 0, 1, 1, 1, 1, w, w, w^2, 1, w^2, w^2, 0, 1, w, 0, 1, 1, w, 0, 1, w^2, 0, 1, w, w, 1, w, w, 0, 0, 1, 1, w^2, 0, w, 0, 1, w, 1, w, w, w^2, 0, w, 0, w, w^2, 1, 0, w^2, 1, 0, 0, 0, 0, 1, 1, w^2, 0, w^2, w, w^2, w, 0, w, w^2, 1, 0, w, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, w^2, w, 1, 0, 1, w, w^2, 0, 1, 1, w, w^2, w, 0, 1, 0, w, w, w^2, 0, w, 0, w^2, 1, w^2, w, w, 0, w, w, 1, 0, w^2, 1, w, w, w^2, 0, w, w^2, 1, w, 1, 0, w^2, w, w^2, 0, w, w^2, w, 0, w^2, 1, w^2, 0, 1, 1, 0, 1, 0, w, 1, 0, 1, w, w^2, 0, w, 0, 1, w, 0, 0, 0, 1, w, 1, 1, 0, w^2, w, w, w, 1, w^2, 0, 1, w^2, w^2, 1, 1, 1, w ] [ 0, 0, 1, 0, 0, w^2, 0, 0, 0, w, w^2, 1, w, w^2, w^2, w, 1, w^2, 1, 1, 1, 0, 0, w, 1, w^2, 1, 0, w, w^2, w^2, w, w^2, w^2, 0, w^2, w, w, 0, w^2, 1, 0, w^2, 1, w^2, w, w, 1, 1, w^2, 0, w^2, 1, 0, w, w^2, 0, w, w^2, 1, w, w^2, 1, w^2, 1, 1, 0, w, w, 0, w^2, 1, w^2, w, 0, 1, w^2, w, w, 1, w^2, 1, w^2, 0, 0, 0, w^2, w^2, w^2, w^2, w, 0, w, w, w, w, 0, w, 1, 1, 0, w^2, w^2, w, w, w^2, 0, w^2, w^2, w^2, w^2, w, 0, w, 1, w^2, 1, 0, w^2, w^2, 0, 0, 0, 1, 1, w^2, w, 0, 0, 1, w, 0, 0, 1, w, 1, w^2, 0, 1, w, 0, w, 0, w^2, w, w^2, 1, 1, 1, w^2, 0, 0, 0, 0, 0, w, 1, 0, w^2, 0, 1, 1, 1, 1, w, 0, w^2, w, w, w, w, w^2, w^2, w, w, 1, w^2, w^2, w^2, w, w^2, 0, 1, 0, 0, 0 ] [ 0, 0, 0, 1, 0, w^2, 0, 0, 1, w^2, w^2, w^2, w^2, 1, w^2, 0, 0, w, 1, 0, w, w^2, w^2, 1, 1, 0, w, w^2, 0, 0, w^2, 1, w^2, 0, w^2, 1, w, w^2, w, 0, 1, 0, w^2, 0, 1, 1, 0, 0, 0, 0, 1, w, w, w, w^2, 1, w, w^2, w, w^2, 1, w, w, 1, w, 1, w^2, w^2, 0, 0, w, 1, 0, 1, 0, w^2, 1, w^2, w^2, w^2, w^2, 1, 1, 0, 1, 0, w, 0, w, 0, 0, 0, w^2, 0, w, 0, 1, 1, w, 0, 1, w^2, w, 1, 1, 1, w, w, w, 0, w, w^2, w, w, w, 1, w^2, w, 1, w, 1, w^2, w, w^2, w, w^2, 1, 1, w, 0, 0, w^2, 1, w, w, w, w^2, 1, 0, 1, w^2, 0, w, 0, 1, 0, w, 1, w, 1, 0, 1, w, 0, w, w, 1, 0, 1, 0, 0, 0, 0, w^2, w^2, 0, w^2, 0, w^2, 0, 1, 0, w, 1, w^2, 1, w^2, 0, w^2, 0, w^2, w, 1, w^2, 0, 1 ] [ 0, 0, 0, 0, 1, 1, 0, 0, 1, w, 1, w, 0, 0, w, w, w, 0, w, 1, 1, 1, w^2, 1, w^2, 1, 1, w^2, 0, 1, w^2, 0, 0, 1, w, w, 0, 1, w^2, 1, w^2, 0, 1, 1, w^2, w^2, 1, w, w^2, 0, w^2, 0, 0, w, 0, w^2, w, 1, w, 1, 1, 1, w, 1, w, w, w, w, w^2, 1, w, 1, 1, w^2, w, w, 1, w^2, w^2, 1, 1, 1, 0, 1, w^2, 0, 0, 0, w^2, w, w^2, w, 1, 0, 1, 1, 0, 1, 0, w^2, w, 0, 1, 0, 1, w, 1, w^2, 1, w^2, 0, 1, w, w, 1, w, 1, w^2, w, w, w^2, 0, 1, w^2, 0, 1, w^2, w^2, 0, 1, 0, 1, w^2, 1, 1, w, 1, w^2, 1, 1, 0, w^2, 0, 0, w, 0, w^2, 1, 1, 1, w, 0, 0, w^2, w^2, w, 1, 1, 0, w^2, w^2, 0, 0, w^2, 0, 0, 0, 1, w, w^2, 1, 0, w, 0, w, w, w, 1, 1, w^2, w^2, w, w^2, w^2, w, w ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, w^2, w^2, w, 1, 1, 0, w^2, 1, 0, w, 0, w, 0, w, w^2, w, 0, w, 0, 1, 1, 1, 1, w^2, 0, 1, 1, w, w^2, 0, 1, w^2, w, w^2, w, w, 1, 1, 0, w, w^2, 0, 1, w, w^2, w^2, w^2, w^2, 0, 0, w^2, 1, 0, w, 0, w, 1, 1, w^2, w^2, 1, w, 1, w^2, 1, w, 1, w^2, w, w^2, w^2, w^2, 0, w^2, 0, w, w^2, 1, 1, w, w^2, 0, w, w^2, 0, w, 1, 0, 1, 0, 1, w, w^2, 0, 1, 0, w^2, 0, w, w, 0, 1, 1, w^2, w^2, 0, 1, w^2, w, 0, w, 1, 1, w^2, w, 0, 0, 0, 0, w, 1, 1, 1, 1, w, w^2, w^2, 0, w, w^2, w^2, 1, w, w^2, w^2, 1, w, w^2, 1, 0, w^2, w^2, 0, 0, w, w, w^2, 0, w^2, w, w^2, 0, 0, 1, 1, 0, w, 0, 0, w, w, 1, 1, 1, w, w^2, w, w, 1, w^2, 0, w^2, 0, w^2, 1, w ] [ 0, 0, 0, 0, 0, 0, 0, 1, 1, w^2, w^2, w, w, w, w, 0, 0, 0, w, w, w, 1, 1, 1, 1, 1, w^2, w^2, w^2, w, w, w, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w, w, w, w, w, w, w, w, 0, 0, 0, w^2, w^2, w^2, w^2, w, w, w, w, 0, 0, 0, 0, 0, 1, 1, w^2, w^2, w^2, w^2, w, w, w, w, w, w, 0, 1, 1, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, 0, 0, 0, 1, w^2, w^2, w^2, w^2, w^2, w, w, w, 0, 0, w, w, w, 0, 0, 0, 0, 0, 1, w^2, w^2, w^2, w, 0, w, w, w, 0, 0, 1, w^2, w^2, w^2, w, w, w, w, w, w, w, w, w, 0, 1, 1, 1, 1, w^2, w^2, w^2, w^2, w, w, 0, w^2, w^2, w, w, 0, w, 0, 0, 0, 0, 0, 0, 1, 1, 1, w^2, w, w, w, 0, w, w, w, 0, 0, 1, 1, 1, w^2, w, w, w, w, w, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [184, 7, 130] Linear Code over GF(2^2) Puncturing of [1] at { 185 .. 186 } last modified: 2010-11-14
Lb(184,7) = 128 is found by truncation of: Lb(192,7) = 136 GW2 Ub(184,7) = 133 DM3
GW2: M. Grassl & G. White, New Codes from Chains of Quasi-cyclic Codes, ISIT 2005.
Notes
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