lower bound: | 153 |
upper bound: | 159 |
Construction of a linear code [220,8,153] over GF(4): [1]: [221, 8, 154] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w, 0, 0, 0, 0, w^2, 0, 0, w^2, w, w^2, w^2, w^2, 0, 1, w, 0, w^2, 1, w, 1, 0, 1, 1, 0, 1, 1, w^2, 0, 0, 1, 0, w^2, w, w^2, w, w^2, 0, 0, 0, 1, 0, 0, 1, 1, 1, w, w, 1, 0, 1, 1, 0, w^2, w, 0, w^2, w, w, w^2, w^2, w, w^2, w, w, w^2, 0, w^2, 0, w, w, 0, w, w^2, w, w^2, 0, w, w, w, w, 1, w^2, 0, w^2, 0, 0, 0, w, 0, w, 0, w^2, w, w^2, 0, 0, w, 1, w^2, w^2, 1, w, w, 0, w, 0, w^2, w, w^2, w^2, 0, w^2, 0, 0, 1, w, 0, w, 1, 1, 0, 1, 1, w, w, w^2, w, w^2, 1, w^2, 0, w, 1, w, w, 1, 0, 0, 1, w^2, 0, 0, 1, w^2, 0, 1, w^2, 0, w, w^2, 1, w, w, 0, 1, w^2, w^2, 1, 1, 1, w, w, w^2, w, 1, w, w, w^2, w, w^2, 0, w, w^2, w^2, w, w^2, 0, w, 1, w, w^2, 0, 0, w, 1, 0, 0, 1, 0, w^2, w^2, w, w, w, w^2, w^2, 0, 1, 1, w^2, w^2, 1, w^2, w^2, 0, w, 1, 1, w, w^2, 0, w, 1, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, w^2, 0, w^2, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, w, 1, 1, w^2, 1, w, 0, 1, w^2, w, w, 0, 0, 0, 0, w, w^2, w^2, 0, 1, w^2, 0, 0, 1, w, 0, 1, 0, 1, 1, w, w^2, w^2, w^2, 0, w, 0, w^2, w, w^2, 0, w^2, w^2, w, w, w^2, w^2, w^2, 1, 0, 1, 0, 0, 0, 1, w, 1, w, 0, w^2, 0, w, w^2, 0, 1, 1, 1, w^2, w^2, 1, w^2, w, w, w, 0, w, w^2, 1, 0, w, w^2, w^2, w^2, w^2, w, w^2, w^2, 0, w, 0, 0, w, 1, w^2, 0, 0, w, w, 1, w^2, 1, w, 0, 0, w^2, w, 1, w^2, w^2, w^2, w, w^2, 0, 1, w^2, 1, w^2, 0, w^2, w, w, 0, 1, 1, w, w^2, w, w^2, 0, 0, 1, 1, 1, w^2, 0, 0, w^2, 0, 0, 1, 1, w, 1, w^2, 0, w^2, w, 1, 0, 1, 0, w, 1, 0, 1, 0, 1, w^2, w, w^2, 1, 1, 1, 0, w^2, 1, w^2, 1, w^2, 0, 1, w, w, 1, w, 0, 1, 1, 1, w, w^2, 1, w, 1, 1, 1, w^2, w, 1, 1, 0, 0, w, 0, 0, w^2, 1, 0, 1 ] [ 0, 0, 1, 0, 0, 0, w, 0, 0, 0, 0, w^2, w^2, w, 0, 0, w^2, w^2, w^2, 1, 0, 0, w^2, 1, 0, 1, w^2, w^2, 1, w^2, 0, 1, w, 0, 1, 1, w^2, 0, 0, w, 1, w^2, w, w^2, w, w^2, w, 1, w, 0, w^2, w^2, w^2, 1, w^2, 0, 1, 0, 0, w^2, 1, w^2, w^2, 1, 1, w^2, 0, w^2, w, w, 0, w, 1, 1, w^2, 1, w^2, 1, 0, 1, w^2, 0, 0, 0, 0, w^2, w, w, 0, 1, w, 0, 1, 0, w^2, w, w, w, w^2, w^2, 1, w, w, w^2, w^2, w^2, w^2, w^2, 0, w^2, 1, w^2, 1, 1, 1, w, 1, 1, w^2, 0, 1, w^2, w, w, w^2, w^2, w^2, 1, 1, w, 0, w^2, 1, w^2, 1, w, 0, w^2, 1, w^2, w, w, 0, 0, 1, 1, 1, w, 1, 1, 1, w, 0, w, 1, w, w^2, w, 0, 1, 0, w^2, w^2, 0, 0, w^2, 0, w^2, w, w, w^2, w, 0, 1, 1, 0, 1, w, 0, w^2, w, w^2, w^2, w^2, 1, 1, w, 1, 1, w, 1, 0, w^2, w^2, 1, w^2, 0, w^2, w^2, 0, w, 0, 1, w, 1, w, 0, w, w^2, 0, 1, w^2, 1, 0, 0, 1, 0, 0, w, 1, w^2 ] [ 0, 0, 0, 1, 0, 0, 1, 0, 0, w, 0, w, w, 1, w, 1, 0, 0, 0, 0, 0, 0, 1, 0, w, w^2, w^2, 0, w^2, w, 1, 1, w, w, 1, 0, 1, 0, w^2, w, w^2, w^2, w, 1, 0, 0, 1, 1, 0, w^2, w, 1, 0, w, w^2, 1, w^2, 1, 1, 0, w, w^2, w, w^2, 0, w^2, w^2, w^2, 0, 1, w, w, w^2, w^2, 0, 1, w, 1, w^2, w^2, w^2, 1, w^2, w, w, 1, 0, w, w, 0, w, 1, 1, 1, 0, 1, w, 0, w, 1, 1, w, 0, w, w, 1, 0, 0, w, 0, 1, w^2, 1, w, 1, w^2, 1, w, w, w^2, 0, w^2, w, 1, 0, w^2, 0, w, w, w^2, 0, w, 0, w, 1, w^2, 1, w, w, w^2, 0, w, w, 1, 0, 1, 1, w, 0, w^2, w, w^2, 1, w^2, w, w, w, 1, 0, w^2, w, 0, w^2, w^2, 1, 1, w^2, 0, 0, w^2, w, w, w^2, w^2, 0, 1, 1, w, 1, w^2, 1, 0, w^2, w, 1, w^2, w^2, w, w, w^2, 0, 1, 0, 0, 0, 1, 0, 1, w^2, w^2, w^2, w^2, w, 1, w, 0, 1, 1, w, w, w^2, w^2, w^2, w, 0, w^2, 1, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, w, 1, w^2, 0, 0, 0, w^2, w, w^2, w, w^2, 1, w^2, 1, 0, 1, w, w, w^2, 0, w, 0, w^2, w^2, w, w, w^2, 1, 1, 1, w^2, w^2, w^2, w, 1, 0, 0, w, 1, w, 0, w^2, w, w^2, w^2, w, w^2, w, w^2, w^2, w^2, w^2, w^2, w, w, 1, w^2, 0, 0, 0, w^2, 0, w^2, w^2, 1, w^2, 1, 1, w^2, w^2, w^2, w^2, 1, w, w^2, w^2, 1, w, 0, 1, 0, w, 0, w, 0, 0, w, 0, 1, 0, w, w, w, w, 0, 0, w, 1, 0, w, 1, w^2, 0, 1, w, w, w^2, w, 1, w^2, w^2, 1, w^2, 1, w^2, w, 0, w^2, w, 1, w^2, 0, w, w, 0, 0, w^2, 1, 1, w, w, 1, 1, 0, w^2, 0, 1, w, 1, w, 0, 0, w, 0, 0, 0, w^2, w^2, w, w^2, 1, w, w^2, w, w^2, w^2, 0, w, 1, w^2, w, 0, w, w, 1, w^2, 1, 1, 1, w^2, 1, w, w, 0, 0, w^2, 1, 1, w, 0, 1, w, w^2, w, 0, w, w^2, 1, w^2, 1, 0, 0, 0, w^2, w, w, w, 0, w, w, w, w, 1, 0, w, w, w^2, w^2, w, w^2, 0, w^2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, w, 1, w^2, 0, w^2, 0, 0, w, w, w^2, 1, w^2, w, w^2, w, w^2, w, 0, w^2, w, w^2, w, w, w, w, 0, w^2, w, w^2, 0, 1, w^2, w, 1, w, 1, w, w^2, 0, w^2, 1, w, 0, 0, 0, w, 0, w, w^2, 0, w^2, 0, w, w, 1, w, w, w^2, 1, w, 1, 1, w, 0, w^2, w, 1, 0, w^2, 1, w, 1, w, w^2, w^2, w, w^2, 1, 0, 1, 0, 0, w^2, w^2, 1, w, w^2, w, 1, w^2, 0, 0, w, w^2, 1, w^2, 1, w^2, 0, 0, 1, w^2, w^2, w, 1, w^2, 1, w, 0, 0, w, w, 0, w^2, 0, w^2, 0, 0, w, 0, w^2, 0, w, 1, 0, w^2, 0, 0, w, 0, 0, w^2, w, w^2, 1, w^2, 0, 1, w^2, w^2, 0, w, 0, 1, 1, w, 0, w, 0, 1, 1, 1, 0, w^2, w, w, w, 1, w^2, 1, w, w, w, w, w^2, w^2, 1, w, 1, w^2, w^2, w, 0, w^2, w, w, w, 0, 1, 0, w^2, 1, w, 0, 1, 1, 1, w, w, 1, w, w^2, w^2, 1, 0, 0, w, 1, w^2, 0, 0, 0, 0, w, 1, w, 0, w, w, w^2, 0, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, w, 0, w, w^2, 0, w^2, 0, 1, 1, 1, w^2, w^2, w, 0, w^2, 1, 0, w^2, w, w, w, 1, 0, w, 0, 0, w^2, w, w, w^2, w, w, w^2, 0, w^2, w, w, w, 1, 1, w, w, 0, w, w^2, 1, 1, w, w, w, w^2, w, 0, w, w, w, w, w^2, 1, 1, 0, 1, 1, 0, 0, w, w, 0, w^2, 1, w, 1, 1, w^2, w, w, 1, w, 1, w^2, 0, 1, w^2, 0, w, 1, 1, w, 0, 1, 1, w^2, w^2, w, 0, 0, 1, 1, w^2, 1, 1, 1, 0, 0, 1, 0, 1, 1, w, w^2, 0, w^2, 1, 0, w^2, w, w^2, 1, 1, w, 1, w^2, w^2, w, w, 0, w, w, w, 0, w^2, w, 0, 0, 0, 1, 1, w^2, w^2, 1, w^2, w, 1, w^2, w, 1, 0, w^2, 0, 1, 0, w, w^2, w^2, w^2, 1, 1, 0, 1, w, 1, w^2, w, w, 1, 0, w, w^2, 0, w^2, 1, w, 0, w^2, 0, w, 0, w^2, w^2, w^2, 0, w^2, w, 1, w, 0, w, w, w, w, 1, w, 1, w, w^2, 0, w, 1, w, w, w, w^2, w, 1, w^2, 0, 0, 1, 1, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, w^2, 0, w^2, 0, 1, 1, 0, 0, w^2, w^2, 1, 1, w^2, w, w, w, 0, w^2, 1, 0, w^2, w, w, 1, 1, 0, w^2, 0, 0, 1, 1, w^2, 0, w, 1, 0, 1, 0, w, 0, w^2, w^2, w, 0, w, 1, w, w, w^2, 1, w, 1, 0, w^2, w^2, w^2, w, w^2, w^2, 1, 0, w, w, w, w^2, 1, 1, 1, w, 0, 1, 1, w, 1, w^2, 1, 1, 0, 0, 1, w^2, w, 0, w^2, 1, 1, w^2, 1, 0, w, w, 0, w^2, w^2, w^2, 1, 1, 0, 0, w^2, 1, 1, 1, 1, 0, w^2, w^2, 1, 0, 1, 0, w, 1, w, w^2, 1, w, w^2, 1, 1, 0, w, w^2, w^2, w, 1, w^2, 1, 0, 0, w, w^2, 0, 0, w^2, 0, 1, w^2, 1, w, 1, 1, 1, 0, w, w, w, w, 1, 0, 0, 0, w^2, 1, w, 1, w^2, w, 1, 0, 1, 1, w^2, 1, w, w, 0, w^2, w, w^2, 1, w^2, 1, 0, w^2, 0, 0, 1, w^2, w, w, w, 0, 1, w, 1, 0, w, 1, w, 1, 1, w^2, 0, w^2, w^2, w^2, w^2, 1, 1, w^2, 1, 1, 0, 0, 0, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [220, 8, 153] Linear Code over GF(2^2) Puncturing of [1] at { 221 } last modified: 2012-08-21
Lb(220,8) = 150 is found by truncation of: Lb(221,8) = 151 MSY Ub(220,8) = 159 is found by considering truncation to: Ub(217,8) = 156 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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