lower bound: | 80 |
upper bound: | 83 |
Construction of a linear code [116,7,80] over GF(4): [1]: [116, 7, 80] Linear Code over GF(2^2) Code found by Axel Kohnert and Johannes Zwanzger Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, w^2, 1, 0, w, 0, w^2, w^2, 1, 1, w^2, w^2, w^2, w^2, 1, w, w, w, w, w^2, w^2, 1, 0, w, w, w^2, w, 0, 1, w, 0, 0, w^2, 0, w, w^2, w^2, 0, 1, 0, 0, 0, w, 0, 0, 0, w^2, 0, w^2, 1, 0, 0, 1, w^2, w^2, w, w, 1, 1, 1, 1, 1, w^2, 1, w^2, 1, 1, w^2, 1, w^2, 1, w^2, w, 1, w, w, w, w, 1, 1, w^2, 1, w, w^2, w, w^2, 1, w^2, 0, 0, 1, w, 1, 1, w, w^2, 0, w^2, w^2, 0, 1, 0, 0, 0, 1, w^2, w^2, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, w, w, w^2, 0, 0, 0, 0, 1, 0, w, w^2, 0, 0, w, w^2, w^2, 1, w, w^2, 1, 0, 1, 1, w^2, 0, w^2, w, w, 1, 0, w, 0, w^2, w^2, 1, w, w^2, w^2, w, w, w^2, 0, w, 0, w, 1, w, 1, w^2, 1, w, 1, w^2, 0, w, 0, w^2, w, w, w, 1, 0, 0, 0, w^2, 0, w^2, 1, 1, w^2, w, w^2, w^2, 1, 0, w^2, w, w, w, w^2, w^2, w, w^2, w^2, w^2, 1, 0, 0, w, 0, 0, w^2, w^2, w^2, 0, 1, 0, 1, w, w, 1, 1, 1, w, 1, 1, w^2, w ] [ 0, 0, 1, 0, 0, 0, 0, 1, 0, w, w^2, w, 0, 0, w, 0, 1, w^2, w^2, w^2, 1, 1, 0, 0, 1, w, w, 1, w, w^2, 0, w^2, w^2, 0, w^2, 1, w^2, w, 1, w^2, 0, w^2, 1, 1, 1, w, 0, 1, 0, 1, w^2, w^2, 1, w, 1, 1, 1, 1, 0, w^2, w^2, w^2, 0, 0, 1, w^2, w^2, w^2, 1, 0, w^2, w, 1, w, w, w, 1, w^2, 1, 1, w, w, w^2, w, 1, w, w, 1, 1, 1, w, w, w, 0, w, w, w, 0, w^2, 0, 1, 0, 0, 1, w, w^2, 1, w^2, w^2, w, 0, w^2, 1, w^2, 1, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, w, w, 0, w, 1, 0, 0, 1, 1, w, 0, w, w, 1, 0, 1, w^2, w, 0, w^2, 1, 0, 0, 0, 1, w, 1, w^2, 1, 1, 1, w, w^2, 1, 0, 1, w^2, w^2, w, 1, 1, 1, 1, w, 1, 0, 0, w, 1, w^2, 1, 1, 1, 0, 0, w^2, w^2, 0, w^2, w^2, w, w^2, 0, w, 0, 1, 1, w^2, 0, w, w^2, 1, w, w^2, w^2, w, 1, w^2, 1, 1, w^2, 0, w, 1, w, 0, w^2, 0, 0, w^2, w^2, 1, 1, w^2, w^2, 0, 0, 1, w^2, 1, w^2, 1, 0, 1, w, 1, w, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, w, 0, 0, 0, 1, w, w, w^2, 0, 0, w, w, 1, w, w, w^2, w^2, w^2, w, 0, w^2, 0, w, 0, 1, 0, w, w, 1, w, w^2, 1, w, 0, w, w^2, 1, 0, 1, 1, w^2, w^2, 1, 1, w^2, w, 1, w, w^2, 1, w^2, 0, w^2, w, 0, w^2, 0, 1, w, 1, 1, w, 1, w, w^2, w, 0, 0, w^2, 0, 1, 0, w^2, 0, w, 1, w, w, w, w, 1, w, w, 0, w^2, 1, 1, 0, w, 0, 1, w, w, 0, 0, 1, w, w, w, 1, w^2, 0, w^2, 1, w, 1, w^2, w ] [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, w, 1, 0, 1, 1, 1, w, w^2, 0, w^2, 0, 1, w^2, 1, 0, w, 0, w, w, w^2, w, w, 1, 1, w, w, w, 1, 1, 0, 1, 0, 0, w, w^2, 1, 0, w, 0, 0, w, w, w^2, 0, w^2, w^2, w^2, w^2, w, 1, 1, 0, w, 1, w, 1, w^2, 0, 0, 1, w^2, w^2, 1, w, 0, 0, w, w^2, w, 1, 0, w^2, 1, 0, 0, w^2, 0, 0, 0, 0, w^2, 0, w^2, w, w^2, 1, 1, w, w, w, w, 0, 0, 0, w^2, 1, w^2, w^2, w, 0, 1, 1, w, 1, w, w ] [ 0, 0, 0, 0, 0, 0, 1, 1, w, 0, w^2, 0, 0, w, w, w, w, w^2, w, 1, 1, w, 0, w^2, w, 0, w^2, w^2, 0, w, 0, w, 0, 1, 0, 1, w, w, w^2, 0, w, 1, w^2, 0, w^2, 1, 1, w, w, w, w, w, 1, w^2, w^2, 0, 1, w^2, 0, 0, w^2, w^2, w^2, w^2, w^2, 0, 1, 1, 1, w^2, w, 1, w, 0, 0, 1, 0, w, w, 0, w^2, w^2, w^2, 1, w^2, 0, w^2, w^2, 0, w^2, 0, 1, 1, w, w^2, 0, w, w^2, w^2, 0, 0, 1, 1, 0, 0, w, 0, w^2, 0, 1, w^2, 1, 1, 0, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2009-03-02
Lb(116,7) = 79 is found by truncation of: Lb(117,7) = 80 Gu Ub(116,7) = 83 follows by a one-step Griesmer bound from: Ub(32,6) = 20 is found by considering shortening to: Ub(31,5) = 20 Bou
Gu: T. A. Gulliver, personal communications 1993-1998.
Notes
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