lower bound: | 88 |
upper bound: | 92 |
Construction of a linear code [147,9,88] over GF(3): [1]: [149, 9, 90] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 1, 1, 2, 2, 2, 0, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 1, 1, 0, 0, 0, 1, 1, 2, 0, 0, 0, 1, 0, 0, 1, 2, 0, 2, 1, 2, 2, 0, 1, 0, 2, 0, 1, 2, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0, 2, 1, 1, 0, 2, 0, 0, 0, 0, 2, 2, 1, 1, 2, 1, 0, 2, 0, 2, 0, 0, 0, 1, 2, 1, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 2, 1, 2, 2, 0, 1, 1, 2, 0, 2, 2, 0, 2, 2, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 1, 2, 0, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 1, 0, 1, 2, 1, 0, 2, 2, 1, 0, 0, 2, 1, 0, 2, 2, 0, 2, 1, 2, 1, 2, 2, 0, 2, 2, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 1, 0, 2, 2, 2, 1, 0, 1, 2, 2, 1, 1, 0, 2, 0, 2, 0, 1, 0, 2, 2, 2, 1, 1, 0, 2, 1, 2, 1, 1, 2, 2, 0, 1, 1, 2, 2, 2, 0, 0, 0, 1, 1, 0, 2, 2, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 2, 0, 0, 1, 1, 0, 2, 0, 1, 2, 2, 0, 0, 1, 1, 0, 0, 0, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 1, 2, 0, 2, 0, 1, 1, 2, 2, 1, 2, 0, 1, 1, 2, 1, 0, 0, 2, 2, 0, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 1, 2, 2, 2, 0, 0, 1, 1, 0, 1, 2, 2, 0, 1, 0, 2, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 1, 1, 1, 0, 1, 0, 1, 1, 1, 2, 0, 2, 0, 1, 0, 2, 0, 2, 1, 0, 2, 0, 0, 2, 2, 2, 1, 1, 2, 2, 2, 1, 1, 0, 1, 1, 0, 0, 0, 2, 1, 1, 0, 2, 2, 1, 2, 1, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 2, 1, 1, 1, 2, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 2, 0, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 0, 2, 2, 2, 1, 2, 0, 2, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 2, 1, 0, 1, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 2, 1, 0, 0, 0, 1, 1, 2, 2, 0, 2, 1, 1, 0, 2, 0, 0, 1, 0, 1, 0, 0, 1, 2, 2, 2, 1, 0, 0, 2, 1, 1, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 2, 1, 1, 1, 0, 2, 2, 2, 0, 1, 1, 1, 2, 2, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 2, 1, 0, 2, 1, 2, 2, 1, 1, 0, 0, 1, 1, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 2, 0, 1, 1, 1, 0, 2, 2, 0, 2, 1, 0, 0, 2, 0, 0, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 2, 0, 0, 1, 1, 0, 1, 0, 2, 0, 0, 0, 2, 1, 1, 2, 2, 1, 2, 0, 1, 1, 0, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2, 1, 0, 2, 0, 1, 1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 1, 0, 0, 2, 2, 2, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 1, 2, 2, 0, 2, 0, 2, 2, 1, 0, 0, 0, 2, 0, 1, 2, 1, 0, 2, 2, 1, 2, 1, 1, 2, 0, 2, 1, 2, 1, 2, 2, 0, 1, 2, 1, 2, 1, 1, 1, 0, 2, 2, 1, 1, 1, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 1, 0, 0, 2, 1, 0, 0, 0, 2, 2, 1, 1, 2, 1, 2, 0, 1, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 1, 1, 0, 2, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 1, 0, 2, 0, 0, 2, 1, 0, 2, 2, 2, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 0, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 1, 2, 1, 0, 1, 0, 0, 2, 1, 2, 0, 0, 0, 1, 2, 1, 1, 1, 0, 0, 2, 1, 0, 2, 1, 2, 1, 2, 2, 0, 0, 1, 2, 1, 0, 0, 2, 2, 2, 2, 2, 1, 0, 0, 1, 2, 2, 1, 1, 0, 2, 0, 2, 1, 1, 2, 1, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 2, 2, 1, 2, 2, 1, 1, 0, 0, 1, 0, 0, 1, 0, 2, 1, 2, 1, 2, 0, 0, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 1, 2, 2, 0, 2, 2, 0, 1, 0, 0, 0, 2, 1, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 2, 2, 0, 2, 0, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 2, 1, 0, 0, 1, 2, 1, 1, 2, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 2, 0, 0, 2, 0, 1, 0, 2, 1, 0, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 1, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 1, 1, 0, 2, 0, 1, 1, 2, 2, 2, 1, 1, 2, 0, 2, 1, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0 ] [2]: [147, 9, 88] Linear Code over GF(3) Puncturing of [1] at { 148 .. 149 } last modified: 2010-04-28
Lb(147,9) = 86 is found by truncation of: Lb(148,9) = 87 MSY Ub(147,9) = 92 Gur
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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