lower bound: | 68 |
upper bound: | 71 |
Construction of a linear code [100,7,68] over GF(4): [1]: [100, 7, 68] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, w, w^2, 0, 0, 0, 0, 1, 0, 0, w, w^2, 1, w, w^2, w, w, 1, 1, 0, 1, 0, w^2, w^2, w, 0, 1, w, 1, 0, w, 0, 1, 0, 0, w, 1, 0, w, 1, w, w, 0, 0, w, 0, 1, w^2, w^2, w^2, 0, 1, 1, w^2, w^2, w^2, 1, 0, w, w^2, w, w^2, 0, w, 1, w^2, w^2, 0, 1, 1, 1, 1, 0, w^2, w, w, w^2, 0, w, w, 0, w^2, 1, 0, 1, w^2, w^2, 1, w, w^2, 0, w, 1, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 1, w, w, w^2, 1, 1, w, 1, w, 0, 0, 0, w^2, w^2, w, 0, 1, w, w^2, 0, 0, w^2, w^2, w^2, 1, w, w, w^2, w^2, 1, w^2, w, w^2, w^2, 1, w, w, 0, 0, 1, w, 1, 1, 1, w^2, 1, w^2, 0, 0, 1, 0, 1, w, 1, 1, w, 0, 0, w, 1, w^2, 1, 1, w, w, 0, w, w, w^2, w^2, w, w^2, w, w, 1, w, w^2, w, 0, w^2, 1, 0, w^2, 1, 1, w, 0, 1, 0, w^2, w, 1 ] [ 0, 0, 1, 0, 0, 0, 0, w, 1, 0, 0, 0, 0, w^2, 0, 1, 1, 1, w^2, w^2, w^2, 0, w, w, 1, w^2, w^2, 1, 0, 0, w^2, w, w^2, w, 0, 0, 1, 0, 0, 0, 1, w, w, 0, 0, w^2, w, w^2, w^2, 0, w^2, 1, 1, w, w, w, w, w, 0, 0, w^2, 1, 1, w, 0, 1, 0, w^2, w^2, 1, 1, 1, w, w, w^2, 0, w, 1, 1, 0, 1, 0, 0, w^2, w, w, w, 1, 0, w^2, w^2, w^2, w, w, w^2, w, w^2, w, 0, 1 ] [ 0, 0, 0, 1, 0, 0, 0, w, w, w^2, w^2, w^2, w, w, 1, 1, 1, 0, w, w^2, w^2, 0, w, 1, w, 0, 0, w^2, 1, 1, w^2, w, 1, w^2, 1, 0, 1, 1, 1, 0, 1, 1, 1, w^2, w^2, 1, w^2, w, w, 1, w^2, 1, 1, w, w, w, 1, 1, w^2, w^2, 1, w^2, w^2, w^2, 1, 0, 1, w, w, 1, 1, 1, w, 1, 0, w, 0, w^2, 0, 1, 1, 1, 1, w^2, w, 1, 1, w, w^2, 0, 0, 1, 0, w^2, w, w^2, w^2, 1, w, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 1, w, w, 1, 1, 1, 1, w^2, w, 1, w, 1, 1, w, 0, 0, w, w^2, 0, 0, w^2, 1, 0, w^2, w^2, 1, 0, w^2, w^2, w^2, w^2, 1, w^2, w^2, 1, 0, 1, 1, 1, 1, 1, 0, 0, w, 0, w, 1, w^2, 0, w^2, w^2, w^2, w^2, w^2, 1, 1, 0, w^2, w^2, w, w^2, w^2, 0, 1, w^2, w, w, w^2, w^2, 1, 0, 1, 1, w, w^2, 0, 0, w^2, w, 0, 1, w, 1, w^2, 1, w^2, w, w, 0, 1, w^2, w ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w, 0, w, 0, 0, w, 1, w, w, w^2, w, w, w, 0, w^2, 0, 0, w, w, w, w, 0, 1, w, 1, w, 0, w^2, w, w, w^2, w, 0, w, 0, 0, 0, 1, 0, 0, 1, 0, 0, w, w^2, w^2, 1, w^2, w^2, w, 1, 1, w^2, w^2, 0, 1, w^2, w, 1, 0, w, 1, w, 0, w, 1, 0, w, w^2, w^2, 1, w^2, 1, 1, 0, w^2, w^2, 0, 1, w, w^2, 0, w, 1, w, 1, 0, w^2, w, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, w, 1, 0, w, 0, 0, 1, w^2, w^2, 0, w^2, w, 1, w^2, 1, 0, w, 1, w^2, 0, w, w^2, w, w^2, w, 0, 1, w^2, 0, 1, w, 1, 0, 0, w^2, 0, 0, 0, 1, 0, 1, 0, w^2, 1, 1, w^2, 1, 0, 1, 1, 0, w^2, w^2, w^2, w^2, 1, w, 0, 0, w, w, w^2, 1, 0, w^2, 1, w^2, w, w, w, w^2, 0, 1, w, 0, 1, 1, 0, 1, 1, 1, w^2, w, w, w^2, 1, w^2, 1, w^2, 0, w ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2009-03-02
Lb(100,7) = 67 is found by truncation of: Lb(104,7) = 71 Gu Ub(100,7) = 71 follows by a one-step Griesmer bound from: Ub(28,6) = 17 is found by considering shortening to: Ub(27,5) = 17 is found by considering truncation to: Ub(26,5) = 16 BGV
Gu: T. A. Gulliver, personal communications 1993-1998.
Notes
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