lower bound: | 54 |
upper bound: | 56 |
Construction of a linear code [75,6,54] over GF(5): [1]: [75, 6, 54] Linear Code over GF(5) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 2, 1, 3, 2, 2, 2, 0, 0, 1, 3, 1, 3, 4, 4, 0, 4, 3, 3, 1, 1, 1, 1, 1, 1, 0, 2, 0, 3, 1, 0, 2, 0, 0, 3, 1, 1, 3, 0, 2, 0, 0, 0, 2, 3, 3, 4, 3, 3, 1, 4, 2, 2, 4, 1, 3, 4, 0, 4, 1, 4, 4, 0, 1, 3, 1, 0, 4, 3 ] [ 0, 1, 0, 0, 0, 4, 0, 2, 4, 1, 1, 3, 2, 0, 1, 4, 2, 3, 0, 1, 2, 3, 2, 1, 4, 2, 2, 1, 2, 0, 0, 1, 2, 0, 3, 0, 3, 1, 3, 3, 0, 0, 3, 0, 1, 1, 1, 1, 1, 2, 1, 1, 3, 4, 0, 1, 2, 2, 1, 0, 4, 3, 4, 0, 2, 0, 3, 0, 0, 2, 1, 1, 2, 2, 0 ] [ 0, 0, 1, 0, 0, 2, 0, 4, 3, 4, 0, 4, 4, 1, 4, 3, 3, 3, 2, 3, 3, 0, 4, 4, 3, 1, 3, 0, 1, 4, 1, 4, 4, 3, 0, 1, 1, 0, 4, 1, 0, 4, 0, 0, 3, 2, 4, 2, 4, 3, 3, 0, 0, 2, 2, 0, 1, 3, 2, 4, 4, 1, 3, 2, 1, 3, 0, 3, 4, 3, 4, 4, 1, 0, 0 ] [ 0, 0, 0, 1, 0, 1, 0, 4, 3, 3, 1, 0, 0, 2, 2, 1, 3, 3, 3, 4, 1, 3, 4, 3, 0, 3, 4, 3, 1, 4, 4, 0, 2, 3, 2, 0, 0, 4, 1, 2, 3, 3, 1, 1, 1, 0, 1, 4, 0, 0, 0, 4, 3, 0, 4, 2, 2, 3, 2, 1, 3, 0, 1, 4, 4, 3, 2, 1, 4, 0, 0, 4, 1, 0, 4 ] [ 0, 0, 0, 0, 1, 0, 0, 2, 3, 1, 4, 4, 0, 0, 4, 2, 3, 2, 1, 2, 1, 2, 4, 4, 2, 4, 0, 4, 3, 0, 1, 2, 1, 2, 3, 3, 3, 3, 2, 2, 2, 0, 1, 3, 2, 0, 1, 1, 1, 1, 4, 1, 4, 0, 1, 2, 4, 4, 3, 0, 4, 0, 2, 4, 4, 4, 0, 1, 3, 3, 3, 3, 2, 2, 4 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 0, 4, 0, 3, 0, 1, 2, 0, 4, 1, 3, 4, 3, 3, 1, 4, 2, 2, 1, 4, 3, 1, 1, 3, 2, 4, 3, 2, 1, 3, 4, 2, 3, 1, 4, 1, 0, 0, 2, 1, 4, 1, 1, 2, 0, 4, 1, 0, 3, 1, 3, 3, 3, 4, 4, 4, 4, 3, 3, 4, 3, 4, 3 ] last modified: 2008-10-06
Lb(75,6) = 53 is found by truncation of: Lb(78,6) = 56 ARS Ub(75,6) = 56 follows by a one-step Griesmer bound from: Ub(18,5) = 11 is found by considering shortening to: Ub(17,4) = 11 BKM
BKM: I. Boukliev, S. Kapralov, T. Maruta & M. Fukui, Optimal linear codes of dimension 4 over $F_5$, IEEE Trans. Inform. Theory 43 (1997) 308-313.
Notes
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