lower bound: | 39 |
upper bound: | 42 |
Construction of a linear code [64,9,39] over GF(4): [1]: [64, 9, 39] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, 1, w, w^2, 1, 1, 0, 0, 0, w^2, w, 1, w, w^2, 1, w, w^2, w, w, 1, 0, w, 0, 0, w^2, w^2, 0, 0, w, 0, 1, w, w, w^2, w, 1, 1, w^2, 1, w, w^2, 0, 0, 0, 1, 1, w^2, w, 0, 1, 1, 1, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, 0, 1, 0, 0, w, 1, 0, 0, w, w, 1, 0, 0, w, 0, 0, w, w^2, 1, 1, 1, w, 0, w, 1, w^2, 0, 1, w, w^2, 0, w^2, 0, w, 1, w, w^2, 1, 0, 0, w^2, 0, 0, w^2, w, w^2, w, w, w^2, w, w, w, w ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, w^2, 1, 0, 0, w^2, w^2, w^2, w, 1, 0, w, w^2, 1, 0, w, w^2, w^2, w, 1, w^2, 0, 1, 0, 1, w, w, 0, 1, w^2, 1, 1, 1, w, 1, 1, 1, 1, w, 0, 1, 0, w, 0, w^2, 0, w^2, 0, 0, w, w, 1, 1, 1, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, w, w^2, w, w, w^2, w, 1, w^2, 0, w, w^2, w^2, w, 1, 0, 0, w^2, w, 0, w^2, 0, 1, 1, 1, w^2, 1, 1, 1, 0, w^2, 0, w, w^2, 0, 0, 1, w^2, w^2, w^2, w, 0, w^2, 1, w, w^2, w, w, w^2, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, w, 0, w, w^2, w^2, 1, 0, w, w^2, w, 0, 0, w, 1, w, 1, 1, 0, w^2, w^2, 1, w, w^2, w^2, 0, 0, 0, w^2, w^2, w, 1, w^2, w^2, 0, 1, 1, 1, w, 1, 0, 0, w, w^2, w, 0, 1, w^2, w^2, 0, w, 0, w, w, w, w ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, w, w^2, w, w^2, w, 1, w^2, 0, w, w^2, w^2, w^2, w, 1, 0, w^2, w, 0, w^2, 0, 1, 1, 1, w^2, w^2, 1, 1, 0, w^2, 0, w, w^2, 0, 0, 1, w, w^2, w^2, w^2, 0, w^2, 1, w, w^2, w, w, w^2, w, 0, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, w, 0, 0, w^2, 0, w^2, 0, w, 0, 1, w, 0, w, 1, 1, 1, w, 1, 1, 1, w^2, 1, w^2, 0, w, 1, 0, 1, 0, w^2, 1, w, w^2, w^2, w^2, w, 0, w^2, w, 0, 1, w, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, w^2, w^2, w, w^2, w, w^2, 0, 0, w^2, 0, 0, 1, w, w^2, w, w, 0, w^2, 0, w^2, w, 1, 0, w^2, 1, 1, w, w, 1, 1, 1, w^2, w, 0, 0, w, 0, 0, 0, w, w, 0, 0, 1, w, 0, 0, 1, 1, 0, w^2, w, w, w, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, 1, 0, w^2, 1, 1, 0, 0, 0, w^2, w, 1, w, w^2, 1, w, w^2, w, w, 1, 0, w, 0, 0, w^2, w^2, w^2, 0, w, 0, 1, w, w, w^2, w, 1, 1, w^2, w, w, w^2, 0, 0, 0, 1, 1, w^2, w, 0, 1, w^2, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2002-11-02
Lb(64,9) = 38 is found by truncation of: Lb(70,9) = 44 DaH Ub(64,9) = 42 follows by a one-step Griesmer bound from: Ub(21,8) = 10 is found by considering shortening to: Ub(18,5) = 10 Liz
Liz: P. Lizak, Optimal quaternary linear codes, Ph. D. Thesis, Univ. of Salford, Nov. 1995.
Notes
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