lower bound: | 66 |
upper bound: | 68 |
Construction of a linear code [90,6,66] over GF(5): [1]: [94, 6, 70] Linear Code over GF(5) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 1, 2, 2, 3, 0, 3, 0, 0, 2, 0, 2, 0, 2, 4, 3, 3, 1, 3, 1, 4, 2, 0, 1, 3, 0, 4, 4, 1, 2, 0, 1, 1, 0, 4, 3, 2, 1, 0, 4, 2, 4, 4, 1, 0, 1, 1, 2, 3, 2, 2, 1, 0, 4, 2, 1, 3, 0, 3, 0, 2, 0, 2, 2, 4, 2, 4, 4, 3, 2, 0, 3, 4, 2, 0, 4, 3, 2, 4, 3, 2, 1, 3, 2 ] [ 0, 1, 0, 0, 0, 2, 0, 0, 3, 3, 2, 2, 0, 0, 2, 4, 4, 2, 0, 3, 3, 0, 0, 2, 1, 1, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 1, 1, 4, 2, 0, 3, 2, 3, 4, 0, 2, 3, 4, 0, 4, 2, 0, 3, 0, 3, 4, 2, 1, 2, 0, 1, 1, 2, 0, 1, 0, 3, 4, 2, 1, 1, 4, 3, 4, 3, 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 1, 4, 4, 1, 1, 3, 3, 1 ] [ 0, 0, 1, 4, 0, 0, 0, 0, 3, 2, 3, 2, 0, 0, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 4, 1, 3, 2, 4, 1, 2, 3, 1, 4, 4, 1, 4, 2, 3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 2, 4, 0, 3, 2, 0, 3, 3, 2, 2, 2, 2, 3, 3, 0, 2, 3, 0, 2, 3, 3, 2, 2, 3, 3, 2, 2, 3, 4, 1, 4, 1, 2, 3, 0, 1, 4, 0, 0, 1, 4, 0 ] [ 0, 0, 0, 0, 1, 4, 0, 0, 2, 2, 3, 3, 0, 0, 4, 2, 2, 4, 1, 3, 3, 1, 1, 4, 0, 0, 4, 1, 1, 4, 1, 4, 1, 4, 4, 1, 0, 0, 2, 4, 1, 3, 4, 3, 2, 1, 4, 3, 2, 1, 2, 4, 1, 3, 1, 3, 2, 4, 0, 4, 1, 0, 0, 4, 1, 0, 1, 3, 2, 4, 0, 0, 2, 3, 2, 3, 0, 0, 4, 4, 4, 4, 1, 1, 1, 1, 0, 2, 2, 0, 0, 3, 3, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 4, 3, 2, 1, 0, 4, 1, 4, 2, 0, 0, 3, 1, 4, 3, 2, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 3, 2, 3, 2, 2, 3, 2, 3, 1, 0, 0, 4, 0, 2, 3, 0, 4, 4, 1, 1, 2, 3, 2, 3, 1, 0, 0, 4, 0, 2, 3, 0, 4, 4, 1, 1, 2, 3, 3, 2, 4, 1, 0, 0, 4, 2, 2, 0, 0, 3, 3, 1, 4, 2, 0, 3, 2, 0, 3, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 3, 4, 1, 2, 4, 0, 0, 2, 4, 1, 4, 1, 3, 0, 2, 3, 3, 2, 4, 1, 3, 2, 4, 1, 3, 2, 2, 3, 3, 2, 4, 4, 1, 1, 0, 2, 3, 0, 1, 0, 0, 4, 2, 3, 2, 3, 4, 4, 1, 1, 0, 2, 3, 0, 1, 0, 0, 4, 2, 3, 2, 3, 0, 0, 4, 1, 3, 2, 2, 3, 2, 4, 0, 2, 3, 0, 1, 3, 3, 0, 2, 4, 1, 3, 0, 2 ] [2]: [90, 6, 66] Linear Code over GF(5) Puncturing of [1] at { 91 .. 94 } last modified: 2010-11-13
Lb(90,6) = 65 is found by shortening of: Lb(91,7) = 65 is found by truncation of: Lb(100,7) = 74 MSY Ub(90,6) = 68 is found by considering truncation to: Ub(89,6) = 67 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
|