lower bound: | 62 |
upper bound: | 64 |
Construction of a linear code [85,6,62] over GF(5): [1]: [88, 6, 65] Linear Code over GF(5) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 3, 1, 4, 3, 0, 2, 3, 1, 1, 4, 3, 4, 0, 4, 3, 4, 2, 0, 2, 4, 1, 4, 4, 1, 0, 1, 3, 2, 4, 0, 2, 0, 4, 1, 3, 0, 1, 0, 1, 1, 0, 2, 3, 3, 0, 4, 4, 2, 3, 2, 3, 3, 4, 2, 2, 4, 0, 1, 3, 1, 2, 1, 0, 0, 1, 4, 2, 2, 3, 1, 2, 0, 1, 0, 3, 4, 0, 4, 4, 0, 0, 3 ] [ 0, 1, 0, 0, 0, 0, 1, 1, 1, 3, 2, 4, 0, 2, 3, 0, 4, 4, 2, 2, 0, 4, 0, 2, 4, 1, 4, 3, 4, 1, 3, 0, 1, 2, 4, 3, 1, 1, 1, 2, 4, 4, 1, 0, 1, 2, 0, 3, 2, 0, 3, 1, 3, 1, 0, 3, 2, 3, 4, 4, 4, 1, 2, 2, 4, 4, 0, 0, 1, 1, 0, 3, 0, 3, 1, 0, 0, 1, 2, 4, 1, 3, 2, 0, 0, 1, 2, 0 ] [ 0, 0, 1, 0, 0, 0, 2, 2, 1, 2, 3, 4, 3, 4, 1, 3, 3, 0, 0, 1, 1, 1, 4, 4, 2, 0, 4, 4, 1, 1, 2, 3, 4, 1, 4, 2, 3, 1, 0, 3, 2, 2, 1, 4, 0, 0, 3, 0, 0, 0, 3, 1, 2, 0, 3, 1, 1, 4, 2, 4, 3, 3, 1, 0, 2, 1, 1, 4, 3, 1, 3, 4, 3, 3, 4, 3, 3, 1, 0, 1, 3, 0, 1, 1, 2, 3, 3, 3 ] [ 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 3, 4, 4, 4, 0, 1, 3, 3, 0, 0, 2, 2, 4, 0, 3, 3, 4, 3, 3, 3, 1, 0, 4, 0, 1, 1, 4, 0, 1, 3, 0, 2, 2, 2, 3, 2, 1, 1, 3, 2, 3, 2, 1, 4, 0, 3, 3, 3, 3, 2, 3, 0, 1, 4, 0, 0, 3, 0, 4, 1, 3, 4, 2, 0, 3, 1, 2, 3, 0, 1, 1, 1, 4, 3, 3, 0, 1, 4 ] [ 0, 0, 0, 0, 1, 0, 1, 3, 0, 3, 1, 2, 0, 0, 4, 0, 0, 2, 2, 2, 1, 1, 4, 4, 3, 0, 0, 1, 3, 2, 1, 4, 2, 0, 2, 4, 0, 4, 3, 0, 0, 3, 0, 1, 4, 3, 2, 4, 2, 4, 3, 2, 2, 3, 2, 0, 4, 2, 1, 0, 2, 1, 3, 1, 1, 3, 2, 1, 3, 3, 1, 4, 1, 2, 0, 4, 1, 4, 0, 3, 0, 0, 1, 2, 3, 3, 3, 4 ] [ 0, 0, 0, 0, 0, 1, 0, 3, 1, 3, 0, 4, 0, 0, 1, 1, 1, 4, 4, 4, 0, 0, 2, 2, 3, 1, 1, 0, 3, 4, 0, 2, 4, 1, 4, 2, 0, 2, 3, 1, 1, 3, 1, 0, 2, 3, 4, 2, 3, 1, 2, 3, 4, 3, 4, 1, 2, 4, 0, 1, 4, 0, 2, 4, 0, 3, 4, 0, 3, 3, 0, 2, 0, 4, 0, 1, 4, 1, 1, 3, 1, 1, 0, 4, 3, 3, 3, 2 ] [2]: [85, 6, 62] Linear Code over GF(5) Puncturing of [1] at { 86 .. 88 } last modified: 2009-01-13
Lb(85,6) = 61 is found by shortening of: Lb(86,7) = 61 MSY Ub(85,6) = 64 is found by considering truncation to: Ub(84,6) = 63 LP
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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