lower bound: | 131 |
upper bound: | 136 |
Construction of a linear code [213,9,131] over GF(3): [1]: [214, 9, 132] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 0, 2, 0, 1, 0, 1, 0, 0, 1, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 0, 1, 0, 2, 1, 2, 0, 1, 2, 2, 1, 2, 2, 0, 0, 2, 2, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 2, 2, 1, 2, 2, 1, 0, 0, 2, 0, 1, 2, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 2, 1, 2, 2, 0, 2, 2, 0, 0, 2, 1, 2, 2, 0, 2, 1, 0, 1, 1, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 1, 2, 2, 0, 0, 2, 1, 2, 1, 1, 2, 0, 0, 1, 2, 1, 2, 2, 2, 1, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 1, 2, 0, 2, 2, 1, 0, 2, 1, 2, 0, 1, 1, 0, 2, 0, 0, 1, 0, 0, 0, 1, 2, 0, 2, 0, 1, 2, 0, 1, 2, 2, 1, 0, 2, 1, 0, 0, 0, 2, 1, 1, 2, 0, 1, 2, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 1, 2, 2, 0, 0, 0, 1, 2, 2, 1, 1, 2, 0, 0, 1, 1, 2, 0, 0, 2, 1, 1, 0, 0, 2, 1, 2, 2, 0, 0, 2, 2, 1, 1, 0, 1, 0, 1, 1, 0, 2, 0, 2, 0, 2, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 2, 1, 2, 2, 0, 0, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 0, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 2, 0, 2, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 1, 1, 0, 2, 2, 1, 1, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0, 1, 2, 1, 0, 2, 0, 2, 0, 2, 1, 0, 2, 0, 1, 0, 1, 2, 1, 2, 1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 0, 2, 2, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 2, 2, 0, 1, 2, 2, 2, 1, 2, 0, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 0, 1, 1, 2, 0, 0, 0, 1, 2, 2, 0, 1, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 2, 2, 2, 1, 1, 1, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 2, 0, 2, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 1, 0, 1, 2, 2, 1, 0, 0, 1, 2, 1, 0, 1, 1, 2, 0, 2, 1, 0, 0, 2, 1, 1, 0, 2, 2, 2, 0, 0, 0, 2, 1, 2, 1, 2, 2, 2, 1, 0, 0, 1, 1, 2, 1, 1, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 1, 1, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 1, 1, 0, 2, 1, 1, 0, 0, 1, 1, 2, 1, 1, 0, 2, 2, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 1, 2, 1, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 0, 1, 2, 0, 2, 2, 2, 0, 2, 2, 1, 1, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 0, 2, 0, 1, 0, 1, 2, 0, 1, 2, 1, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 2, 1, 1, 1, 1, 0, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 0, 2, 2, 1, 0, 0, 0, 2, 0, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 1, 2, 2, 0, 1, 0, 0, 1, 0, 2, 2, 1, 1, 2, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 0, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 0, 1, 0, 2, 1, 2, 2, 0, 0, 0, 0, 1, 2, 1, 2, 2, 0, 1, 0, 1, 0, 0, 2, 2, 1, 1, 0, 0, 1, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 2, 0, 1, 0, 2, 1, 1, 2, 1, 1, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 1, 1, 2, 2, 0, 2, 2, 0, 0, 2, 1, 1, 1, 2, 1, 1, 0, 0, 1, 0, 1, 2, 1, 1, 2, 2, 1, 1, 1, 0, 2, 2, 0, 2, 2, 2, 0, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 1, 2, 0, 1, 2, 1, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 1, 0, 1, 0, 2, 1, 2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 1, 2, 1, 0, 1, 0, 2, 0, 0, 1, 0, 2, 1, 1, 0, 1, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 1, 2, 1, 0, 2, 2, 1, 2, 2, 1, 2, 1, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1, 1, 1, 1, 2, 0, 1, 0, 1, 2, 2, 0, 1, 2, 1, 0, 0, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 1, 1, 0, 1, 2, 2, 1, 2, 0, 2, 1, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 1, 0, 1, 0, 1, 2, 0, 1, 0, 2, 1, 0, 2, 2, 2, 2, 1, 1, 0, 1, 1, 2, 2, 0, 2, 1, 0, 2, 1, 1, 2, 0, 1, 0, 2, 1, 2, 2, 2, 2, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 0, 1, 2, 2, 2, 0, 2, 2, 1, 1, 1, 0, 1, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 0, 2, 0, 1, 1, 1, 2, 2, 2, 2, 0, 1, 1, 0, 2, 1, 2, 1, 0, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 1, 2, 1, 0, 0, 1, 2, 1, 0, 1, 1, 2, 0, 1, 1, 2, 0, 2, 1, 1, 2, 1, 0, 0, 1, 1, 2, 1, 0, 2, 0, 1, 2, 1, 1, 0, 2, 2, 2, 0, 0, 0, 2, 1, 2, 0, 1, 1, 1, 0, 2, 1, 2, 0, 2, 2, 0, 1, 1, 2, 2, 0, 0, 1, 0, 1, 1, 1, 0, 2, 0, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 2, 2, 2, 1, 1, 1, 0, 2, 0, 2, 0, 2, 2, 2, 1, 0, 2, 2, 2, 0, 1, 1, 0, 2, 2, 2, 1, 2, 1, 0, 0, 1, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 2, 1, 0, 2, 0, 1, 2, 0, 2, 1, 1, 1, 0, 0, 0, 2, 1, 0, 2, 2, 2, 1, 1, 1, 2, 0, 2, 1, 1, 1, 1, 2, 2, 1, 1, 0, 0, 2, 1, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 0, 1, 2, 2, 0, 2, 2, 0, 1, 2, 1, 0, 1, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 2, 1, 2, 2, 0, 2, 2, 1, 1, 1, 2, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 0, 2, 2, 1, 2, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 2, 2, 1, 2, 1, 0, 1, 1, 0, 2, 1, 2, 0, 0, 1, 0, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 2, 0, 0, 2, 0, 0, 0, 1, 0, 2, 1, 2, 0, 1, 2, 1, 0, 2, 1, 1, 0, 1, 2, 1, 0, 1, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 2, 2, 1, 1, 2, 1, 2, 1, 1, 0, 2, 2, 1, 0, 1, 2, 1, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 0, 2, 2, 1, 2, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 0, 2, 1, 1, 1, 2, 0, 1, 2, 0, 1, 0, 0, 1, 0, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 2, 2, 1, 1, 2, 0, 2, 1, 0, 1, 1, 2, 2, 2, 1, 1, 2, 1, 0, 2, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 0, 2, 1, 1, 2, 1, 1, 2, 2, 0, 2, 2, 0, 2, 1, 0, 2, 0, 0, 0, 1, 0, 0, 1, 1, 2, 0, 0, 0, 2, 2, 2, 1, 0, 1, 0, 2, 1, 0, 0, 2, 1, 2, 2, 2, 2, 1, 0, 2, 2, 2, 1, 0, 2, 0, 2, 1, 2, 2, 2, 1, 2, 2, 0, 0, 2, 0, 2 ] [ 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 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, 1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 1, 1, 1, 1, 1, 1, 1 ] [2]: [213, 9, 131] Linear Code over GF(3) Puncturing of [1] at { 214 } last modified: 2009-03-02
Lb(213,9) = 129 is found by shortening of: Lb(214,10) = 129 is found by truncation of: Lb(216,10) = 131 MSY Ub(213,9) = 136 is found by considering truncation to: Ub(212,9) = 135 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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