lower bound: | 60 |
upper bound: | 62 |
Construction of a linear code [88,7,60] over GF(4): [1]: [88, 7, 60] 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, 1, 0, w, w^2, 1, w, w^2, 1, 0, 0, 0, 0, 1, w^2, w, w^2, w, w^2, w^2, 0, 0, 1, w, w, 0, 0, w, w, 1, 0, 0, 1, 1, 1, w^2, w^2, w^2, 1, w, 1, 0, w, w, 0, w^2, w^2, 1, 0, w, w^2, 1, w^2, 1, 1, 0, w^2, w, w, w, 1, 0, w, 0, w, 1, w^2, w^2, w, w^2, w, w^2, w^2, w, 0, w, 0, 1, 0, 1, 1, 0, w ] [ 0, 1, 0, 0, 0, 1, 1, 0, 0, w, w^2, 1, w, 1, 1, w, 0, w, w^2, 0, 0, 1, 1, w, w, 0, 1, w, w, w^2, 0, w, w, 0, 0, 1, w, w^2, 1, 1, 0, w^2, 1, 0, 0, 0, w, 1, w^2, 0, 1, w, 1, 1, w, 1, w, w^2, 1, 0, 1, w, 0, w, w^2, w, 0, w^2, 0, w^2, w^2, 1, 1, 0, 0, 1, 1, w^2, w^2, w^2, w, w, 0, 0, 1, w^2, w, w^2 ] [ 0, 0, 1, 0, 0, w^2, w^2, 0, 0, 0, w^2, 0, w, w^2, 1, w^2, 0, w, 1, 1, w, w, 0, w^2, 1, 1, w, w, 1, 0, w, 1, 1, w^2, 1, w, 0, w^2, 0, w^2, w, 0, w, 1, 0, 0, w^2, 1, 1, w^2, w^2, w^2, 1, w^2, w, 0, 0, w^2, 0, w, w^2, w, 0, w^2, w, w, 0, 0, 1, 1, w, w, 0, 0, 1, 1, 1, 0, 0, w, 1, w^2, w^2, w, w, w^2, w^2, 1 ] [ 0, 0, 0, 1, 0, 0, w^2, 0, w^2, 0, 1, w, w, w, w^2, 1, 0, w, w, 0, w, 1, 0, w^2, w, w^2, 1, 0, w^2, 0, w, 1, w, w^2, w^2, 0, w^2, w, 0, 1, 0, w^2, w^2, 0, 1, w, 0, w^2, w, 1, 0, 0, 1, w^2, w^2, w^2, w^2, 1, w, 0, w, w, 1, w, 0, w^2, w, 0, w^2, 1, 1, w^2, 1, 0, 1, 0, w, 1, w^2, w^2, 1, 1, 1, 1, 1, w^2, w^2, 1 ] [ 0, 0, 0, 0, 1, w^2, 0, 0, w^2, w, 1, w^2, 0, w, w, 1, 0, w, 0, 1, w^2, 1, w, 0, w^2, w^2, w^2, 1, 1, w^2, 0, 1, w, w^2, 0, 1, 0, w^2, 0, w, w^2, 1, 0, 1, w, 1, w, 0, w^2, w^2, w^2, 1, 1, 1, w^2, w, 1, w, 0, 0, w, w^2, 0, 0, 1, w, w, 0, 0, w, 0, 1, 0, w^2, w, 1, w, w^2, 0, w, 0, w, w^2, 1, w, w, 1, w ] [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, w, w, w, w, 1, 0, w^2, 1, w, 0, 0, 1, 0, w, w^2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2007-09-28
Lb(88,7) = 58 is found by truncation of: Lb(91,7) = 61 Gu Ub(88,7) = 62 follows by a one-step Griesmer bound from: Ub(25,6) = 15 is found by considering truncation to: Ub(23,6) = 13 BGV
Gu: T. A. Gulliver, personal communications 1993-1998.
Notes
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