lower bound: | 156 |
upper bound: | 162 |
Construction of a linear code [224,8,156] over GF(4): [1]: [224, 8, 156] 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, w^2, 0, 1, w^2, w, w^2, w, w, w, w, w^2, 1, w, w^2, 0, w, 1, 0, 1, 1, 0, 0, w, 0, 1, 0, 1, 0, 0, w, w, 1, w, 0, w, 0, 1, 1, w^2, 1, 0, w, w^2, 0, 0, 1, 1, 1, 0, w^2, w^2, w, 1, w^2, 0, 1, w^2, 1, w^2, w^2, w, 1, 0, 1, 1, 1, 1, 0, w, 0, 1, 0, 1, w^2, 0, w, 0, w, w^2, 0, w, w^2, 1, w, 1, w, 1, 1, w, 0, 1, 0, w^2, w, w, w, w^2, w, w, 1, w, w^2, w, 1, w, 0, w^2, 0, 0, 1, w^2, 1, 0, w^2, w, 0, w^2, 0, w^2, w, w^2, w, 0, 0, w, 1, 1, w^2, w^2, w^2, w^2, w^2, 0, 0, w, 0, 1, w^2, 0, 1, w^2, 0, w, w, 0, w, 0, w, w^2, w^2, w, 1, w, w^2, 1, w, w, 1, w, w^2, w, 1, w, 1, 1, 0, 0, 0, 1, 1, w, 0, w, 1, 1, 0, 1, 1, 0, 1, w, 0, w, w, 0, w, w, w, 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, 0, w, w, 1, w^2, w^2, 0, w^2, 1, w, 0, 1, w, 0, 0, w^2, w^2, w, w^2, w, w^2, 0, 1, w^2, w, w^2, 1, 1, 0, w^2, w^2, 1, w, w, 0, 1, 0, w, w, 0, 1, w, 1, 0, 1, 0, 0, w^2, 0, 0, w^2, 0, w^2, 1, 0, w, 1, w, 0, w^2, 1, 1, 1, w^2, 0, 1, w, 1, w^2, w, 1, 0, w^2, w, w, 0, w^2, 1, 0, w, w^2, 0, w^2, w, w, 0, w, 1, 0, 0, w^2, 0, w, w^2, 1, 1, 0, w, 0, 1, 1, 1, w, 0, 0, 0, 0, w^2, 0, w^2, 0, 0, 0, w^2, 1, w, w^2, w, 1, 0, w, w^2, w, 0, w^2, w^2, w, 1, 0, 1, w, 0, 1, w^2, 0, 0, 0, w, 1, 0, 1, w, w, w^2, 0, 1, 1, w, w, 1, 1, 0, w^2, 1, 1, 1, 1, 0, 1, 1, w^2, 0, 1, w^2, 0, 0, 1, w, w^2, w^2, 0, w, 1, 1, w, w, 0, 0, w^2, w^2, w, w, w^2, w, w^2, w^2, 1, 1, 0, w, 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, w, w^2, w, w^2, 0, w, w^2, 1, 0, 1, 1, w^2, 1, 0, w^2, 0, 1, w, 1, 0, 0, 1, 0, 1, 1, w^2, w, 0, 1, 1, w^2, w^2, 1, 1, 1, 1, 1, w^2, w^2, w, w, w^2, w^2, w^2, w^2, 0, 1, 1, w^2, 0, w^2, 1, 1, w, 0, 1, 1, 1, 0, 1, w^2, w, w, w, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, w, w^2, w^2, w, 0, 1, 0, w^2, w, 0, w^2, w^2, w^2, 0, 1, 0, 0, w^2, w^2, 0, 1, w^2, 0, 0, w, w, w^2, w, 0, w, 1, w^2, w^2, 0, 1, 1, 0, w^2, w^2, w^2, w, 0, w^2, w, 0, w^2, w, w, w^2, 1, w, 0, 0, w^2, 1, w, w, w^2, w^2, w, w, w, 1, 0, w^2, 0, 1, w, w, w^2, 1, w^2, 0, w^2, 1, 1, 1, 0, 1, w^2, w^2, w, 1, w^2, w, w^2, 1, 0, w^2, 0, 0, w^2, w^2, w^2, w^2, 0, 1, w, w^2, 0, w^2, w^2, w^2, w^2, 0, w, w, 0, 1, 1, w, w^2, 1, 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, w, w^2, w^2, 1, 1, w, 0, w^2, w, w^2, w, w, 1, 0, w^2, w, w, 0, w^2, 1, 1, w, 1, w, w^2, w^2, 0, 1, w^2, 1, w^2, 1, w^2, w^2, w^2, 0, 1, w^2, w, 1, w, w, 0, w^2, w^2, w^2, 0, w, 0, w, w, w^2, 0, 0, w, 0, w^2, 1, 0, w^2, w, w, w^2, w, 0, 0, 0, 1, w^2, w, 1, 1, 1, 0, 1, w^2, w, w, 0, w^2, w^2, w, w, w^2, 0, w^2, 0, w^2, 1, w^2, w^2, 1, 0, w, w^2, w^2, w^2, w, 0, w^2, 1, w, 1, 1, w, 1, w, w^2, 0, w^2, 1, w^2, w, w^2, w, 1, w, 0, w^2, w^2, w, w^2, 1, w^2, 0, 0, 1, w, w^2, w, w^2, w^2, 0, w^2, 0, w^2, 1, 0, 0, w^2, w^2, 0, w, w^2, w, w^2, w, w^2, w^2, w, w, w^2, 1, 0, 1, w^2, 1, 1, 0, 1, w^2, w^2, 1, w^2, w^2, 0, w, w^2, 1, 1, w, 1, w^2, w, w, 0, w, w^2, w^2, w, 0, w^2, w^2, 0, 1, 1, 1, w, w, w^2, 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, w^2, w, 1, w, 1, 0, 1, 0, w^2, 1, w, 0, w^2, 1, 1, w, 0, 0, 0, 0, w, w^2, w^2, 0, w^2, 1, 1, w^2, w^2, 0, 1, 1, 0, 1, 1, 1, 0, w^2, w^2, w^2, w^2, w, w^2, 0, 0, w, w, 0, w^2, 0, 0, w^2, 1, w, w, w^2, w^2, w^2, w, 0, w^2, 1, 1, w, w, w^2, 1, 0, w^2, w^2, w, 1, w^2, w, w^2, 1, 0, 0, w^2, w, 1, w, w^2, w, 0, 0, 0, w, 0, 0, 1, 1, 0, 1, w^2, w, 1, w^2, w, w, 0, w^2, 0, 0, 0, 0, w, 1, w, w^2, w, w, 0, w^2, 0, w, w, 1, 0, w^2, w, w^2, w, 0, w^2, 1, 1, w, 0, w^2, w^2, w^2, w, w, 0, w, 1, w, 1, 1, w^2, 0, 1, w^2, w, w, w^2, w^2, 1, w, w^2, w, w^2, 1, 1, w, 0, 1, 0, 0, 0, 0, w, 0, w^2, 1, 1, 1, w^2, 1, w, w, w^2, w^2, w^2, w, w, w, 1, 1, 1, w, w, w^2, w^2, w^2, w^2, w, 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, 1, 1, 1, 1, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, w^2, w^2, w^2, w^2, w, w, 1, 1, 1, 1, 1, 1, 0, 1, 0, w^2, w, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, 1, 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, 1, 1, 1, 1, 0, 0, w^2, 0, 1, 1, w, 0, 0, 1, w, w, 1, w^2, w^2, w, 0, 0, 0, w^2, w, 1, w^2, w^2, 1, w, 0, w^2, w^2, 1, 1, w^2, 0, 1, w^2, 0, w, w, w^2, 1, w, 0, 0, w, 1, w, 0, 1, 1, 0, 0, 1, w, w^2, w^2, w^2, w, 1, 1, w^2, w, w, 1, w, w, w, w, 0, w^2, 0, 0, w, 0, w, w^2, w^2, w^2, 0, w^2, w, w^2, 0, w^2, w^2, w, 0, w^2, w, w^2, w, w^2, w, w, 0, 0, 0, 1, 1, w, 0, w, w, w^2, w^2, w^2, 0, w, 1, 0, 0, w, 1, w, 0, w^2, w, 1, 1, 0, w^2, w, w^2, 0, 1, 1, w, 1, w, 1, 0, w^2, 1, 0, w, w^2, w, w^2, 1, w, w^2, w, 0, 1, w, w^2, 1, 1, w^2, 0, w^2, 1, 0, 0, 0, 1, w, w, 1, w, w^2, 0, 0, w^2, 0, w, w^2, 0, 1, w^2, 0, 1, 1, 1, w^2, 0, w, w, 1, w^2, 0, 1, 0, w, w, w, 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, 1, 1, 1, 1, 0, 0, w^2, 1, 0, 0, w^2, 1, 1, 0, w^2, w^2, 0, w, w, w^2, 1, 1, 1, w, w^2, 0, w, w, 0, w^2, 0, w^2, w^2, 1, 1, w^2, 0, 0, w, 1, w^2, w^2, w, 0, w^2, 1, 1, w^2, 0, w^2, 1, 0, 0, 1, 1, 0, w^2, w, w, w, w, 1, 1, w^2, w, w, 1, w, w^2, w^2, w^2, 1, w, 1, 1, w^2, 1, w^2, w, w, w, 1, w, w^2, w, 1, w, w, w^2, 1, w^2, w, w^2, w, w^2, w, w, 0, 0, 0, 1, 1, w, 0, w, w, w, w, w, 1, w^2, 0, 1, 1, w^2, 0, w^2, 1, w, w^2, 1, 1, 1, w, w^2, w, 1, 0, 0, w^2, 1, w, 1, 0, w^2, 1, 0, w, w, w^2, w, 0, w^2, w, w^2, 1, 0, w^2, w, 0, 0, w, 1, w, 0, 1, 1, 1, 0, w^2, w, 1, w, w^2, 0, 0, w^2, 1, w^2, w, 1, 0, w, 1, 0, 0, 0, w, 1, w^2, w^2, 0, w, 1, 0, 1, w^2, w^2, w^2, w, 1, w, w^2, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2008-09-06
Lb(224,8) = 153 is found by truncation of: Lb(225,8) = 154 MSY Ub(224,8) = 162 is found by considering truncation to: Ub(221,8) = 159 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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