lower bound: | 159 |
upper bound: | 165 |
Construction of a linear code [228,8,159] over GF(4): [1]: [229, 8, 160] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, w, 0, 0, 0, w, 0, 0, 0, 0, w, w^2, 0, w^2, 0, w, 0, w, 1, 0, 1, 1, w^2, w, w, w^2, w^2, 1, w, 1, 1, 0, 0, 0, w, w^2, 0, 0, w^2, 1, 0, w^2, w, w^2, 0, 0, w^2, w, w^2, 1, w^2, w^2, w^2, w, w, w, w^2, w, w^2, 1, 0, 1, 0, 1, 0, w^2, w, w^2, 1, w, 0, w, 1, w^2, 1, w^2, 1, 1, w^2, 1, w, 1, 1, 0, 1, 0, 0, w^2, 0, 0, 0, 0, w^2, 1, 1, 1, 0, 1, w, 1, 1, 0, w, w^2, w^2, 1, 1, w, w, w, w, w^2, 1, 1, w, w^2, 0, 0, w, 0, 0, 0, 0, w^2, 1, w^2, w, 0, w, 1, 0, w^2, w, w^2, w^2, w^2, 1, 0, 1, w^2, 0, 1, w^2, w^2, w^2, w, 0, w^2, 0, 0, 1, w^2, w^2, 0, w, 1, 1, w, w^2, 0, w, w^2, 0, w, 0, 1, 1, w, w, w^2, 1, 1, w, w^2, w, 0, 0, w^2, w, w^2, 1, 0, 0, w^2, w^2, 1, w^2, 1, 0, w^2, 0, 1, w^2, 0, w^2, 1, w, w, 1, 1, w^2, 1, w^2, 0, w, 1, 1, 0, w^2, 0, w^2, 1, 1, 0, w, 1, 1, 1, 0, w ] [ 0, 1, 0, 0, 0, 0, 0, w^2, 0, 0, 0, w, 0, 1, 0, w^2, w^2, 1, w^2, w^2, w^2, w^2, w^2, w, w, w^2, w, w, 0, w, w^2, 0, w^2, 0, w^2, 0, 1, 0, w, 0, 1, 0, w^2, 0, w, w^2, w, w, w^2, w, w, w, w, w, 1, w^2, 0, 0, w^2, 0, 1, w^2, w, w^2, w, w, 0, w, w^2, 0, 0, 0, 1, w^2, w, w, 1, w^2, w^2, w, 1, 1, 1, w^2, w^2, w, 1, w, w^2, w^2, w, w, w, 0, w^2, w^2, 0, 0, 1, w^2, 1, w, 0, 1, w^2, 0, 0, 0, 0, 0, w^2, w, 1, 1, w, w, 1, 0, w, 0, 1, 1, 1, w^2, 0, w^2, w^2, 0, w, w, w, 0, w^2, 0, w^2, 0, 1, 1, 1, w^2, w^2, 1, w, 1, 0, 1, w^2, 1, 0, w, 1, w^2, 0, w, w^2, w^2, 0, w, 0, w^2, w, 1, 1, w, 0, w^2, 0, w^2, 1, w, w^2, w, w, w^2, w^2, 1, 1, w, w, w^2, 1, w, w, w^2, w^2, w, 1, 1, w, 0, 1, 1, 0, 0, w, w, 0, w^2, 0, 1, 0, 0, w, w, 1, 1, 1, 0, 1, w^2, 1, w, 0, w^2, 1, w, w^2, w^2, w^2, w, 1, 0, w^2, 1, 0, 0, w^2, w^2, w^2 ] [ 0, 0, 1, 0, w, 0, 0, 0, 0, 0, w^2, w, w^2, w^2, 0, w, 0, w^2, w^2, w^2, w^2, w, 1, w, w, 0, w^2, w, 0, w^2, 0, 1, 1, 1, 1, w^2, w^2, 1, 1, 0, 1, w, 0, 1, w, w^2, 1, 0, 1, 0, w^2, 0, 1, w, w, 0, w, w^2, 0, w, w, w, w^2, w^2, 1, w, w^2, 1, 0, w^2, 0, 0, 1, 1, w, 0, w, 0, w, 0, 0, w^2, 0, w^2, 0, w, 0, 1, w, 1, w, 1, 0, w, 0, 0, 1, w^2, w^2, 1, w, 1, 1, 1, w, w^2, w^2, 1, w^2, 1, w^2, 1, w, w, 1, 1, w^2, w^2, 1, 1, 1, w, w, w^2, 1, 1, 1, w^2, w, 1, 1, w, 1, w, 1, w, w^2, 0, w, 0, 0, w, w^2, 0, 0, w, w^2, 0, 0, w^2, 1, 1, 0, w^2, 0, 1, 1, w, 0, 0, w, 0, w^2, 1, w, w^2, w, 1, w^2, 1, w, w, w, 0, w^2, w^2, w, w^2, 0, w, w, 0, 0, 1, w^2, 0, 1, 0, w^2, w^2, w^2, 0, 0, w, 1, w^2, 1, w, w, w, w^2, w, 1, 0, 0, 1, 0, 1, w^2, w, w^2, w^2, w, 1, 1, 0, 1, w, 0, 1, w, 0, 0, 0, 1, 1, w, w^2, 1 ] [ 0, 0, 0, 1, w^2, 0, 0, 0, 0, 0, 0, w, 1, w^2, 1, w, 0, w^2, w^2, w^2, 0, w, w^2, w, w, 0, 0, 0, 0, w, 0, 1, 1, w^2, w^2, w, w, w, w, w, 0, 1, w, 0, 1, 0, 0, w^2, w^2, 1, 0, w, w^2, w, 0, w^2, 1, 0, 1, 0, w^2, 0, w^2, w, 1, w^2, w^2, 1, 0, w^2, w, w, w^2, w^2, w, w^2, w, 1, 1, w^2, 1, 0, w^2, 1, 1, w^2, 1, 1, 0, w^2, w, 1, 1, w^2, w, w, 0, 0, w^2, w^2, w, 1, w, 1, 1, 0, w, 1, 1, w^2, w^2, w^2, w, 1, 1, w^2, 0, 1, 0, w, w^2, 1, w, w^2, w, w, w^2, 0, 1, w^2, 1, w^2, w^2, w, w, w, 0, 1, w, w^2, w^2, 1, 0, 0, 1, 0, w^2, 0, w, w^2, 0, w^2, 1, w, 0, 0, 1, w^2, 1, 1, w^2, w, 1, w^2, w^2, w, w, w, 0, 1, 0, 1, w^2, 0, 0, 1, w, w^2, w^2, w^2, 0, w^2, w^2, 0, 0, w, 1, 1, w^2, 1, 1, 1, w^2, w^2, w^2, w^2, w, 1, 1, 0, w^2, w^2, w^2, 0, w, w^2, w^2, 0, w, w^2, w^2, 1, 0, 0, 1, 0, 0, 0, w^2, 0, w^2, w, 0, 1, 0, w, 1, w^2, 0 ] [ 0, 0, 0, 0, 0, 1, 0, w, 0, 0, 0, w, 0, w^2, 0, 1, w, w, w^2, w^2, w^2, w, w^2, 1, w, 0, w, w, w, w, w^2, 0, w^2, w, 1, 1, 0, w^2, 1, w, 0, w^2, 1, 1, 1, w, w, w^2, 0, w^2, w, w^2, w, w^2, 0, w^2, 0, 1, w, 0, w^2, 1, w, 0, w^2, w^2, 0, 0, w, w, w, w^2, 0, w, w^2, w^2, 1, 0, 0, 0, 1, w, w^2, 1, w^2, w, 0, w^2, 0, 0, w, w^2, 1, 1, 1, w^2, 0, 1, w^2, w^2, 0, 0, w, 0, 1, 1, w, w, w^2, 1, w, 0, 0, 1, w^2, 0, w, w^2, 0, w, 1, 0, 1, w^2, 0, w^2, 1, 0, 1, w^2, 0, w^2, w^2, w, 1, w^2, w^2, w, w^2, 1, w, w, w^2, w, 1, 1, w^2, w^2, w, w, w^2, w, 1, w, 1, w^2, w^2, w, w^2, 1, w, w^2, 1, 1, w, w^2, 1, 1, 0, w^2, w^2, 1, w^2, 1, 1, w^2, w, 0, 1, w^2, w, w, 1, w, w^2, 0, w, w^2, w^2, 0, 1, w, 1, 1, w^2, w^2, 0, w^2, w^2, w^2, w, w, w^2, w, 1, w, 0, w^2, 0, 1, 0, w^2, 1, w^2, w^2, 0, 1, w^2, 1, 0, 0, 1, w^2, 0, 1, w^2, 1, w, w^2 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, w^2, w^2, w, w, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, w, w, w, 1, 1, 1, 1, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, w, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w, w, w, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w, w, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w, w, w, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, w, 1, 1, 0, w, w, 0, 0, 1, 0, 1, w, 0, w, w, 0, w, w^2, 1, w, 0, w^2, 1, 0, 1, w^2, 1, w, w, w, w^2, 0, w, w^2, w, w^2, w, 1, 1, 0, w, 0, w^2, w, w, 0, w^2, 0, w, w, w^2, 0, w^2, 0, w, 0, 0, w^2, w^2, w^2, w, w, 1, w, 1, w, 0, 1, w^2, 0, w, 0, 0, w^2, 0, w^2, w^2, w^2, w^2, w, w, w^2, 1, 1, w, 1, w, 0, w, 0, w^2, 0, w^2, 1, w^2, w, 0, 0, 1, w, 1, w^2, 1, w^2, w, w, 0, 0, 0, w^2, 1, 1, w, w^2, w, w^2, w, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, w^2, 0, w^2, w^2, w, w^2, w^2, w^2, 0, 1, 0, w^2, w^2, w^2, w^2, 0, 1, 1, w, w^2, w, w, w^2, 0, w^2, 1, 0, 1, 1, 1, w^2, w^2, 1, 0, w^2, w, w^2, 0, 0, 1, w, 1, w, 0, 0, w, w^2, 1, w^2, 1, w, 1, 1, w^2, w, w, w^2, 0, w, 0, w, 1, 0, w^2, 1, 0, w^2, 1, w, 1, 1, 0, 0, w, w^2, w, w^2, w, 1, w^2, 0, w^2, 1, w^2, w, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, w^2, 0, 0, 1, w^2, w^2, 1, 1, 0, 1, 0, w^2, 1, w^2, w^2, 1, w^2, w^2, 1, w, 1, w, 0, 1, 0, w, 0, w^2, w^2, w^2, w, 1, w, w^2, w, w^2, w, 1, 1, 1, w^2, 1, w, w^2, w^2, 1, w, 1, w^2, w^2, w, 1, w, 1, w^2, 1, 1, w, w, w, w^2, w^2, 0, w^2, 0, w^2, 1, 0, w, 1, w^2, 1, 1, w, 1, w, w, w, w, w^2, w^2, w, 0, 0, w^2, 0, w^2, 1, w^2, 1, w, 1, w^2, 1, w^2, w, 0, 0, 1, w^2, 0, w, 0, w, w^2, w^2, 1, 1, 1, w, 0, 0, w^2, w, w^2, w, w^2, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, w, 1, w, w, w^2, w, w, w, 1, 0, 1, w, w, w, w, 1, 0, 0, w^2, w, w^2, w^2, w^2, 0, w^2, 1, 0, 1, 1, 1, w, w, 0, 1, w, w^2, w, 1, 1, 0, w^2, 0, w^2, 1, 1, w^2, w, 0, w, 0, w^2, 0, 1, w^2, w, w, w^2, 0, w, 0, w^2, 0, 1, w, 0, 1, w, 0, w^2, 0, 0, 1, 1, w^2, w, w^2, w, w^2, 0, w, 1, w, 1, w, w^2, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [228, 8, 159] Linear Code over GF(2^2) Puncturing of [1] at { 229 } last modified: 2008-09-06
Lb(228,8) = 156 is found by truncation of: Lb(229,8) = 157 MSY Ub(228,8) = 165 is found by considering truncation to: Ub(225,8) = 162 DM4
MSY: T. Maruta, M. Shinohara, F. Yamane, K. Tsuji, E. Takata, H. Miki & R. Fujiwara, New linear codes from cyclic or generalized cyclic codes by puncturing, to appear in Proc. 10th International Workshop on Algebraic and Combinatorial Coding Theory(ACCT-10) in Zvenigorod, Russia, 2006.
Notes
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