lower bound: | 159 |
upper bound: | 167 |
Construction of a linear code [232,9,159] over GF(4): [1]: [233, 9, 160] 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, w^2, w^2, 1, 0, 1, w, w^2, 1, 1, 0, 1, w, 0, 0, 1, w, w, 1, 1, 1, w^2, 1, w^2, w, w^2, 1, w, 1, 1, 1, w^2, w, w^2, 1, 0, 1, w^2, 1, w^2, w^2, 1, 1, w^2, 1, 0, 0, w^2, 1, w^2, 1, w, 1, w^2, w^2, w^2, 1, w^2, 0, w^2, 1, 0, w, 0, w, w, w^2, w^2, 0, w^2, 0, 0, w^2, w^2, w, 1, w, 1, 0, 1, w, w, w, 0, 0, w, 1, w, w, w^2, 1, w^2, w, 0, 1, 1, w^2, w^2, w, 1, 0, 0, 0, 1, w, 1, 1, w, 1, w, w^2, w, w^2, 0, 1, 0, 0, w^2, w, w, w, 0, w^2, w, 0, w^2, w^2, 1, w^2, 0, w^2, 1, 0, 1, w, w^2, w, 0, w^2, 1, w, w, w^2, w^2, 0, w^2, 1, w, w^2, w, w, 1, 0, 0, 1, w, 0, 1, 0, 1, 0, 0, w^2, 0, w^2, 1, w^2, w^2, 0, w, w^2, 1, 1, 1, w, w^2, w^2, w, w, 1, w^2, 1, w^2, w, 1, w, 1, w^2, 0, 0, w, w^2, 0, 1, 0, 1, 0, w, w, w^2, 1, 0, 1, w, 1, w, w^2, w, 0, 0, 0, w^2, 0, w, 1, w^2, 1, 1, 1, w, 0, 0, w, w^2, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, w^2, 1, w, 1, w^2, w^2, w^2, 0, 1, w, 1, w, w, w, w^2, 0, 0, 0, w^2, 1, w, w, w, 1, 0, w^2, 0, w, 0, 0, 0, 0, 0, 1, w, 0, 1, 0, 0, 0, w, 0, w, 1, 0, 1, 0, w^2, w^2, 1, w^2, w^2, w^2, 1, 1, w^2, 0, 1, 1, 0, w, w^2, 0, 1, w, 0, w^2, 0, 0, 1, 1, w^2, w, w, w, w^2, w^2, w^2, w, w, w, w^2, w, w^2, 1, 0, 0, w, w, 1, w^2, 0, w, w, 1, w, 0, 0, 0, 0, 1, 0, 1, 0, 0, w, w^2, w^2, w^2, w, w^2, w, w^2, w, 0, 1, 1, w, 0, w^2, w, w^2, 1, 0, w^2, 1, 0, 1, 0, 1, 0, 1, 1, w, w, w, 1, 1, 1, w^2, w^2, w^2, 1, 1, w, 1, 1, w^2, w^2, w, 0, w^2, w, w^2, w, w^2, w^2, w^2, w, w^2, 1, w^2, w^2, w^2, 1, 1, 1, 0, 1, 1, w, 0, w^2, 0, 1, 0, w^2, 0, w, w, 1, 1, w^2, w, 0, 1, 1, w^2, w^2, w, w, w, w^2, w^2, w, 1, 1, 1, w, w^2, 1, 1, 1, 1, w^2, 1, w, w, w^2, 1, w, w^2, w^2, 1, w, w, 1, w^2, w^2, 1, w^2, w ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, w, 1, 1, w^2, w^2, w, w^2, w^2, 0, 0, w, w^2, w^2, w^2, 1, w^2, w, w, w, 1, w^2, 0, 0, 0, 1, w^2, 1, 0, w^2, 1, 1, 1, 1, 0, w^2, w, 1, 1, w, 0, 1, 0, 1, 1, w^2, w^2, 0, w^2, w, 0, 1, w^2, w, 1, 1, w^2, 1, w, 0, 1, w^2, w, 0, 0, 1, 1, 0, w, 1, w^2, w^2, w^2, w, 0, 0, w, 1, w, 1, 0, w, 1, w, w^2, w, 0, w, w^2, 0, w, 1, w^2, w^2, w, 0, w^2, w^2, 0, 0, 0, w^2, 0, 1, w, 1, 0, 1, w, w^2, w, w^2, w^2, 0, w^2, 1, w, 1, 1, 1, 0, 0, 1, 0, 0, w^2, 0, 1, w, w^2, w^2, 1, 1, 1, 0, 1, w, 1, w^2, w^2, 0, 1, w^2, w, w, 0, w^2, w, w, w, w, w^2, w, 1, w^2, 1, w, 1, 0, 0, 0, w^2, w^2, 1, 0, 0, w, 0, 1, w, w^2, w^2, 1, w, w^2, w^2, 0, 1, 0, 1, w^2, 0, 1, 1, 0, w^2, w^2, 1, 1, w, w, 0, w, 1, 0, w^2, 1, 1, 1, w^2, 0, 0, w^2, 1, w^2, w^2, w^2, w^2, 1, w^2, w, 1, w, w^2, w, 0, 0, w, 0, w, w^2, w, 0, w^2, w^2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, w, w, 1, 1, 1, 0, 1, 1, 1, 1, 0, w^2, w, w, 1, w^2, w, w, w^2, w^2, w^2, w, w, w, w^2, 1, w, 0, 0, 0, w, w^2, w, 0, 1, w^2, w, 0, w, 1, 1, w, 0, w^2, 1, 1, w^2, 1, w^2, w^2, w, w, 0, w, w, w, 1, w, 0, w, 0, 0, 1, w^2, w, 0, w, w, w, 1, w^2, w^2, w^2, 1, 1, 0, 1, w, w^2, w, 1, w, w^2, 0, w^2, 0, w, 0, 0, 0, 1, w^2, w, 1, 1, 0, w^2, w, 0, 1, w, 1, 1, w, 0, w, w, 1, 0, 0, w, 1, 0, 1, 0, 0, 1, 1, w, w, 0, w, 0, w^2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, w, w^2, 1, 0, w, 0, w, 1, 0, 0, w, w, 0, 1, 1, w, 0, w^2, w, 1, 0, 0, w, w^2, w, w^2, 0, w, w, 0, 1, 1, 0, w, w^2, 0, w, w, 1, w^2, 0, w^2, 1, 1, w, 0, w, 0, w^2, w, 0, 1, 1, 0, 1, 1, w^2, w^2, w^2, w^2, 0, 0, w, w^2, 1, 1, w^2, 1, w^2, w^2, 0, 1, w, w^2, w, w^2, w, w^2, w^2, 1, w, w^2, w, 1, 1, w, 1, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, w^2, 0, w, 0, w^2, w^2, w^2, 1, 0, 0, w^2, 0, 1, 1, w^2, 1, w, w^2, 0, w^2, 1, w^2, 0, 1, w, 0, 1, w, 1, 1, w^2, w^2, w, 1, 0, w, w, w^2, w, w, w^2, w, w^2, w, 1, w, 0, 0, w, w, 0, w^2, w, w^2, 0, w^2, 0, w^2, w^2, 1, 1, w, w, w^2, w^2, 1, 1, w^2, w^2, 1, w, 1, 1, w, 1, w^2, w, w, w^2, w, w^2, 0, w, 1, w, w^2, w, w^2, w^2, w^2, w, w^2, w^2, 1, 0, 0, w^2, 1, 1, 1, 0, 1, w^2, 1, w^2, 0, w, w^2, w^2, 0, w, w, 1, 1, 0, 1, w^2, w, 0, 1, w, 1, w^2, 1, w^2, w, 1, w, 1, w^2, w, w^2, w, 1, w, w, 1, w^2, 1, w, w^2, 0, 1, w, 1, w^2, 0, w^2, w^2, 0, w^2, w, 0, 0, w^2, 0, w, 0, 0, 0, w, 0, w^2, w^2, 0, 1, 0, w^2, 0, 0, w, 1, 0, 1, 0, 1, w^2, 1, w, 0, 0, w^2, 1, w, w, w^2, 0, w, 1, 0, 1, w, w^2, 0, 1, 1, w^2, 1, 1, w, w^2, 1, w, w, w, 0, 1, 1, 0, w^2, 0, 0, w^2, 0, 1, 1, 0, w, 1, w^2, w, w^2, w, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, w^2, w, 1, w^2, w, w, 0, w^2, w, w, 0, 0, 0, w, w, 0, w^2, 0, w^2, w^2, w^2, w^2, w, 1, w^2, 1, 0, w^2, 1, w, w, w, 1, 0, 0, w^2, w^2, w^2, w, 1, 0, 0, 1, w, w, w, 0, 1, w, w^2, w^2, w^2, w, w^2, 1, w^2, w, w, w^2, w, w^2, w, w, w, w^2, w^2, 0, 0, w, 0, w, 1, w, w, 1, 0, w, 0, w, w, 0, 1, 0, 1, w, w^2, w, w, 1, w, w, w^2, 0, w, 0, 1, w, w^2, w, w, 0, w^2, 1, 1, 1, 0, w, w, w^2, 0, w, w^2, w^2, 1, w^2, w^2, 1, 0, 1, w^2, w^2, 0, 0, w^2, w, w, w, w^2, 1, 0, w^2, w, w^2, 1, 0, w, 1, 1, w, w^2, 0, 0, w, w, w, 1, w^2, w^2, w^2, w, 0, w^2, w^2, w, 1, w, 0, w, w, w, 0, 1, w^2, 0, 0, w, w, 1, w, 1, w^2, w^2, 1, 1, 1, w^2, w^2, 0, 1, w^2, w, w, 1, w, 0, 0, 0, 0, w^2, 1, 1, 0, 1, 0, 1, w, 0, w^2, w^2, w^2, 0, w, w, 0, 0, w, 0, 0, w^2, 0, 0, w, 0, 0, 1, w^2, 0, 0, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, w, w^2, 1, w^2, 1, 0, w, w^2, 0, 0, w, w^2, w^2, w^2, 0, 0, 0, w, w^2, w^2, w^2, w, 0, w, w^2, w, w^2, 0, w, w^2, w^2, w, 1, 1, w, 0, w, 1, 0, w, 1, w, 1, 0, w, w^2, w, w, 0, w^2, 1, 0, w^2, w, w^2, 0, w^2, 1, 0, 0, 1, w, 1, w, 1, 1, 1, 1, 1, 0, w^2, w^2, 1, w, w, 0, 1, w^2, w, w^2, 1, w, w^2, w, 0, 1, 1, w^2, w^2, w, 0, 0, w, 0, w^2, 0, w^2, w, 1, 0, w^2, 0, 1, w^2, 0, 1, 0, w^2, w, w^2, 0, w^2, w, w^2, w^2, 1, w^2, w^2, w^2, 1, 1, w, w^2, 1, w^2, 1, 1, 0, 1, w, w^2, w, w, w^2, 0, 0, 0, w^2, 0, 0, 1, w^2, w^2, w^2, w, 0, w, 1, w^2, 0, 0, 1, w, w, 1, 1, w^2, 0, w, w^2, 1, w^2, w^2, w^2, 1, w, 0, 1, 1, 1, 0, w, 0, 0, 1, w^2, w^2, 0, 0, w, w^2, w^2, w, 1, w^2, w^2, 0, w, 0, w, 0, 0, 1, w, 1, 1, w, w^2, w^2, w, 0, w^2, 0, w, 0, 1, 1, w, 1, 1, 0, 0, 1, w, w, w, 1, 1, w^2, w, 1, w, 1, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, w, 1, w^2, w^2, w^2, 0, w^2, 0, 1, 1, w, w, 0, 0, w^2, w, 1, w, w, w, 0, w^2, 1, 1, w, 0, w^2, 1, w, 1, w, 0, 1, 1, 0, 1, 0, w^2, 1, w, 0, w^2, w^2, w, w^2, 1, 1, w, w, w^2, 0, 1, w^2, 0, 0, 0, 0, 0, 1, 0, 1, 0, w, w, 1, 1, w^2, 1, 0, w^2, 0, w^2, 0, 1, w, w, 0, 0, w, 1, w, w, 1, w, 1, w, w^2, 1, 0, w, 1, w, 0, w^2, 1, 0, 1, w^2, w, w^2, 1, 0, w, 0, w, 0, 1, 0, w^2, w^2, w, 1, 0, 0, w^2, 0, 1, w^2, 1, 0, 1, 0, w^2, w, w, 1, w, w^2, 0, 0, 0, w, 0, w^2, 1, 0, w, w, 1, w^2, 0, w^2, 1, w, 1, 1, w^2, w^2, w, 0, 1, 0, 1, w, 1, w^2, w, w^2, w^2, w^2, 1, w^2, 0, w, 1, w^2, w, w^2, w, w^2, 0, 0, w^2, 0, w, 1, 1, 0, 1, w^2, 0, 1, 1, 1, w^2, w, w, 1, 1, w^2, w^2, 0, 0, w, 1, 1, w, w, w^2, w, 1, 1, 0, w^2, 0, 0, 1, w, 1, w, 1, w^2, 0, w^2, 1, w, 1, 0, w^2, 1, 1, w^2, w^2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, 0, w, w, w, 1, w, 1, 0, 0, w^2, w^2, 1, 1, w, w^2, 0, w^2, w^2, w^2, 1, w^2, 1, 1, w, 0, w^2, 1, w, 1, w, 0, 1, 0, 1, 0, 1, w, 0, w^2, 1, w, w, w^2, w, 0, 0, w^2, w^2, w, 1, 1, w^2, 0, 0, 0, 0, 1, 0, 1, 0, 1, w^2, w^2, 0, 0, w, 0, 1, w, 1, w, 1, 0, w^2, w^2, 1, 1, w^2, 0, w^2, w, 1, w, 1, w, w^2, 1, 0, w, 0, w^2, 1, w, 0, 1, 0, w, w^2, w, 0, 1, w^2, 1, w^2, 1, 0, 1, w, w, w^2, 1, 0, 0, w^2, 0, 1, w^2, 1, 0, 0, 1, w, w^2, w^2, 0, w^2, w, 1, 1, 1, w^2, 1, w, 0, 1, w^2, w^2, 0, w, 1, w^2, 1, w, 1, 1, w^2, w^2, w, 0, 1, 1, 0, w^2, 0, w, w^2, w, w, w, 0, w, 1, w^2, 0, w, w^2, w, w^2, w, 1, 0, w^2, 0, w^2, 0, 0, 1, 0, w, 1, 0, 0, 0, w, w^2, w^2, 1, 1, w^2, w^2, 0, 0, w, 1, 0, w^2, w^2, w, w^2, 0, 0, 1, w, 1, 1, 0, w^2, 0, w^2, 0, w, 1, w, 0, w^2, 0, 1, w, 0, 0, w, w^2, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [232, 9, 159] Linear Code over GF(2^2) Puncturing of [1] at { 233 } last modified: 2012-08-21
Lb(232,9) = 157 is found by shortening of: Lb(233,10) = 157 is found by truncation of: Lb(240,10) = 164 GW1 Ub(232,9) = 167 is found by considering shortening to: Ub(231,8) = 167 is found by considering truncation to: Ub(229,8) = 165 DM4
GW1: M. Grassl & G. White, New Good Linear Codes by Special Puncturings, ISIT 2004 Chicago USA June 27 - July 2 2004.
Notes
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