lower bound: | 88 |
upper bound: | 90 |
Construction of a linear code [124,6,88] over GF(4): [1]: [124, 6, 88] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w^2, w, 1, 0, 0, w, 1, w, 0, 0, w^2, w^2, w^2, w^2, w^2, w, w, 1, 0, w^2, w, 0, 1, 0, 1, w^2, 0, w^2, w^2, w, w, w, 1, 1, 0, 1, 1, 1, w, w, w^2, 0, w^2, 1, w^2, w, 1, w, w, 0, 1, w, 1, 1, 0, w^2, w, w, w^2, w, 0, 1, 0, 1, 1, 0, 1, w, w^2, 1, 1, 1, 1, w^2, 0, w^2, w, 1, w, w, w, 1, 0, w, w, w, w, 0, w^2, 0, 1, w, w, w^2, w, 1, 1, 1, w, 1, w^2, 1, 0, w, 0, w, w, w, 1, w, 0, 0, 1, 0, 0, w^2, 1, w ] [ 0, 1, 0, 0, 0, 0, w, w^2, w, 1, 0, 0, w^2, 1, w, 0, 0, w^2, 1, w^2, w^2, w^2, w, w, 0, 0, w^2, w, 0, 1, w, 1, w^2, 0, w^2, w^2, 1, w, w, 1, 1, 0, 0, 1, 1, w, w, w^2, w, w^2, 1, w^2, w, 1, 1, w, 0, 1, w, 1, w, 0, w^2, w, w, w^2, 0, 0, 1, 0, 1, 1, 1, 1, w, w^2, 1, 1, 1, 1, w^2, 0, w^2, w, w, w, w, w, 1, 0, 0, w, w, w, 0, w^2, 0, 1, 0, w, 1, w, 1, 1, 1, w, w, w^2, 1, 0, w, 0, 0, w, w, 1, w, 0, w, 1, 0, 0, w^2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, w, w^2, w, 1, 0, w^2, w^2, 1, w, 0, 0, w, 1, w^2, w^2, w^2, w, 1, 0, 0, w^2, w, 0, w^2, w, 1, w^2, 0, w^2, 0, 1, w, w, 1, 1, w^2, 0, 1, 1, w, w, 1, w, w^2, 1, w^2, w, 1, 1, w, 0, 1, w, w^2, w, 0, w^2, w, w, 1, 0, 0, 1, 0, 1, 1, 1, 1, w, w^2, 1, w, 1, 1, w^2, 0, w^2, 0, w, w, w, w, 1, w^2, 0, w, w, w, 0, w^2, 0, w, 0, w, 1, w, 1, 1, 1, 0, w, w^2, 1, 0, w, 0, 0, w, w, 1, w, 1, w, 1, 0, 0, w^2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, w, w^2, w, 1, 0, w^2, w^2, 1, w, 0, w, w, 1, w^2, w^2, w^2, 0, 1, 0, 0, w^2, w, w^2, w^2, w, 1, w^2, 0, 1, 0, 1, w, w, 1, w, w^2, 0, 1, 1, w, w, 1, w, w^2, 1, w^2, w, 1, 1, w, 0, 1, w, w^2, w, 0, w^2, w, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, w, w^2, w^2, w, 1, 1, w^2, 0, 1, 0, w, w, w, w, 0, w^2, 0, w, w, w, w, w^2, 1, w, 1, w, 1, w, 1, 1, w, 0, w, w^2, 1, 0, w, 0, 0, w, w, 1, w^2, 1, w, 1, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 1, 0, 0, w, w^2, w, 0, 0, w^2, w^2, 1, w, w^2, w, w, 1, w^2, w^2, w, 0, 1, 0, 0, w^2, 0, w^2, w^2, w, 1, w^2, 1, 1, 0, 1, w, w, w, w, w^2, 0, 1, 1, w^2, w, 1, w, w^2, 1, 1, w, 1, 1, w, 0, w, w, w^2, w, 0, w^2, 0, 1, 1, 0, 0, 1, w^2, 1, 1, 1, 1, w, 0, w^2, w, 1, 1, w^2, w, 1, 0, w, w, w, w, 0, w^2, 0, w, w, 0, w, 0, 1, 1, 1, w, 1, w, 1, 0, w, 0, w, w^2, 1, 1, w, 0, 0, w, w, 0, w^2, 1, w, 1, 0 ] [ 0, 0, 0, 0, 0, 1, w, 1, 0, 0, w, w^2, w, 0, 0, w^2, w^2, 1, w^2, w^2, w, w, 1, w^2, w^2, w, 0, 1, 0, 0, w^2, 0, w^2, w^2, w, 1, w, 1, 1, 0, 1, w, 1, w, w, w^2, 0, 1, 1, w^2, w, 1, w, w^2, 0, 1, w, 1, 1, w, w^2, w, w, w^2, w, 0, 1, 0, 1, 1, 0, 0, w, w^2, 1, 1, 1, 1, w^2, 0, w^2, w, 1, 1, w, w, 1, 0, w, w, w, w, 0, w^2, 0, w, w, 0, w^2, 0, 1, 1, 1, w, 1, w, 1, 0, w, 0, w, w^2, w, 1, w, 0, 0, w, 0, 0, w^2, 1, w, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2002-10-15
Lb(124,6) = 88 is found by truncation of: Lb(128,6) = 92 Koh Ub(124,6) = 90 follows by a one-step Griesmer bound from: Ub(33,5) = 22 is found by considering shortening to: Ub(32,4) = 22 GH
Koh: Axel Kohnert, email, 2006.
Notes
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