lower bound: | 95 |
upper bound: | 103 |
Construction of a linear code [165,11,95] over GF(3): [1]: [166, 11, 96] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 2, 0, 0, 2, 1, 0, 0, 0, 2, 2, 1, 2, 0, 2, 1, 1, 1, 2, 1, 1, 2, 1, 0, 1, 1, 2, 2, 0, 1, 1, 0, 0, 0, 1, 0, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 1, 2, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 1, 2, 1, 1, 0, 2, 2, 2, 0, 0, 2, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 1, 2, 1, 1, 1, 2, 2, 2, 0, 2, 0, 1, 1, 1, 0, 1, 2, 2, 0, 1, 0, 1, 0, 2, 0, 2, 1, 2, 0, 0, 1, 1, 0, 2, 0, 2, 0, 1, 1, 1, 2, 2, 2, 1, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 2, 0, 1, 2, 1, 0, 1, 2, 2, 1, 2, 2, 0, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 2, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 2, 1, 2, 2, 0, 1, 1, 0, 1, 1, 2, 0, 2, 0, 2, 1, 1, 1, 1, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 1, 1, 1, 0, 0, 1, 1, 2, 0, 1, 2, 1, 1, 1, 2, 0, 2, 2, 0, 1, 1, 0, 0, 1, 1, 2, 0, 2, 0, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 0, 1, 0, 0, 2, 1, 2, 1, 0, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 0, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 1, 1, 2, 0, 0, 1, 2, 2, 0, 0, 0, 0, 2, 1, 1, 2, 2, 2, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 1, 0, 1, 2, 2, 2, 2, 2, 1, 1, 0, 2, 1, 1, 2, 2, 1, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 0, 2, 0, 0, 2, 1, 1, 2, 2, 2, 0, 0, 0, 1, 2, 2, 1, 1, 2, 0, 0, 2, 0, 0, 2, 2, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 1, 0, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 1, 2, 2, 0, 0, 1, 1, 1, 1, 2, 1, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 1, 1, 0, 1, 1, 0, 1, 0, 2, 2, 1, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 0, 1, 2, 0, 0, 2, 1, 1, 1, 0, 2, 0, 0, 1, 2, 0, 1, 1, 0, 2, 1, 1, 2, 2, 0, 2, 2, 1, 0, 2, 1, 0, 2, 2, 1, 1, 1, 0, 0, 1, 2, 1, 1, 0, 2, 2, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 0, 1, 1, 0, 0, 2, 1, 2, 2, 2, 2, 0, 1, 0, 1, 0, 0, 0, 2, 1, 2, 2, 1, 1, 0, 2, 1, 2, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 2, 1, 2, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 1, 2, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 1, 2, 2, 2, 0, 0, 1, 0, 2, 1, 2, 1, 1, 0, 1, 0, 0, 2, 0, 0, 1, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 2, 0, 1, 1, 0, 0, 2, 1, 1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 2, 2, 2, 2, 2, 0, 1, 0, 1, 1, 2, 1, 1, 1, 0, 2, 2, 2, 1, 0, 2, 1, 1, 0, 1, 0, 0, 2, 0, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 1, 0, 2, 0, 1, 2, 1, 1, 1, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 1, 1, 0, 2, 0, 1, 0, 2, 2, 2, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 0, 0, 1, 1, 1, 0, 2, 0, 2, 0, 0, 2, 1, 1, 2, 1, 0, 1, 1, 2, 2, 1, 1, 1, 2, 2, 0, 1, 2, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 0, 0, 1, 2, 1, 2, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 0, 0, 1, 1, 2, 0, 2, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 2, 0, 0, 2, 2, 1, 0, 1, 0, 0, 1, 0, 2, 0, 1, 0, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 0, 2, 2, 0, 0, 1, 1, 2, 1, 1, 2, 0, 1, 0, 1, 1, 2, 2, 2, 2, 0, 1, 0, 0, 2, 2, 1, 2, 2, 2, 0, 2, 2, 0, 1, 0, 0, 1, 2, 2, 0, 0, 2, 2, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 2, 0, 1, 1, 2, 1, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 1, 0, 2, 2, 0, 0, 1, 2, 0, 1, 0, 0, 2, 2, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 0, 2, 2, 1, 0, 2, 2, 1, 1, 1, 2, 0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 1, 0, 1, 0, 1, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2, 2, 1, 1, 0, 2, 1, 2, 1, 2, 2, 1, 0, 0, 2, 2, 1, 2, 1, 2, 1, 0, 2, 0, 0, 2, 2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 1, 0, 2, 1, 0, 2, 1, 1, 0, 1, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 1, 2, 0, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 0, 2, 1, 1, 0, 0, 1, 2, 2, 2, 2, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 0, 0, 1, 2, 1, 1, 2, 1, 2, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 2, 2, 1, 2, 0, 2, 0, 1, 1, 0, 2, 2, 0, 0, 2, 1, 0, 0, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 1, 1, 2, 0, 1, 0, 2, 0, 1, 1, 0, 2, 0, 2, 2, 0, 2, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 2, 0, 2, 0, 1, 2, 2, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 0, 1, 2, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2, 1, 0, 2, 2, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 1, 2, 0, 2, 1, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0, 0, 2, 2, 0, 2, 2, 0, 0, 1, 0, 2, 2, 0, 2, 1, 2, 2, 1, 1, 2, 2, 0, 2, 0, 1, 1, 2, 1, 2, 1, 0, 1, 0, 2, 2, 0, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 0, 2, 1, 0, 0, 2, 2, 1, 1, 2, 2, 2, 0, 0, 1, 1, 2, 0, 1, 2, 1, 0, 1, 0, 2, 0, 2, 2, 1, 1, 0, 2, 0, 2, 2, 2, 1, 0, 1, 0, 2, 0, 0, 2, 0, 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, 1, 1, 1, 1, 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, 0, 0, 1, 1, 1, 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, 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, 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, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1 ] [2]: [165, 11, 95] Linear Code over GF(3) Puncturing of [1] at { 166 } last modified: 2009-08-13
Lb(165,11) = 94 MSY Ub(165,11) = 103 is found by considering shortening to: Ub(163,9) = 103 is found by considering truncation to: Ub(162,9) = 102 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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