lower bound: | 130 |
upper bound: | 132 |
Construction of a linear code [180,6,130] over GF(4): [1]: [180, 6, 130] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 1, 1, 0, 1, 1, w^2, w^2, w, w, 1, 1, 0, w, 0, w^2, 1, 1, 0, 0, w^2, w^2, 1, 1, 0, 0, w^2, w, 1, w^2, 0, w^2, 0, w^2, w^2, w, w, w^2, w^2, w^2, 1, 1, 0, w^2, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, w^2, 0, w, w, w, 0, w^2, w, 1, 1, w, 0, w^2, 1, 1, w^2, w^2, w, 1, 1, 1, w^2, w, 0, w, 1, 0, 1, w, 0, w, w, 1, 0, 0, w, w^2, w, w, 0, w, 0, w^2, w, 0, 0, w, w, w, 0, 1, 1, 1, w, 1, 0, w, w^2, w^2, 1, 0, w^2, w, w, 1, w^2, 1, 0, 0, w^2, 1, w^2, 0, w^2, w^2, w, w, 0, w, w, 1, 0, w^2, w, w, 0, w, w, 1, w^2, w^2, w^2, w^2, w, 0, 1, w, 0, 1, 1, w, w, w, 1, w^2, 0, w, 1, 1, 1, w^2, 0, 1, 1, w^2, 0, 0, 1, w^2, 1, w, w ] [ 0, 1, 0, 0, 0, w^2, 0, 1, 0, 0, 1, 1, w, 0, w, 0, 0, w^2, w, w, w^2, w^2, w, w, 0, 1, 0, w^2, w^2, 1, w, w, w^2, 1, w, w, w, w^2, w, 1, w^2, 1, 0, 0, 0, 0, w^2, w, 1, w, w^2, 0, 1, 1, w^2, w, 0, w^2, 1, 1, w^2, 0, w^2, w^2, w, 1, 1, w^2, w^2, w, w^2, w^2, w, w^2, w, w, 1, 0, w, w, 0, 1, 0, w^2, w^2, 1, w^2, w, 1, w, 0, 1, 0, 0, w^2, 0, 1, 0, 1, 1, 1, 1, w, 0, 0, w^2, 0, 0, w, 0, w^2, w^2, 1, w, w^2, w^2, w, 1, 1, w, w^2, 1, 1, w, 1, 0, w^2, 1, w^2, w^2, w^2, w, 1, w^2, w^2, w^2, 1, 0, w^2, 1, 1, 0, 1, 1, w, 1, 1, 1, 0, w^2, w, w, w^2, w, w, w, w^2, w, w, 1, 1, w^2, 1, w^2, w, w, 1, w, 1, 0, 0, w, w, w, w^2, w, 0, 0, w^2, w ] [ 0, 0, 1, 0, w, 0, 0, 0, 1, w, 0, 1, 0, w, 1, 0, 1, 1, 1, w^2, 1, 0, 0, w^2, w, w, 0, 0, w, w, 1, w, w^2, w^2, 1, w, w^2, 1, w^2, w, w^2, 0, 0, w, w^2, w, 1, 1, 1, 1, w, w, 1, 0, w^2, 1, w^2, w^2, 0, w^2, 1, 0, 0, w, w, w, w, 1, 0, 0, 0, w, 0, w, w, w^2, w^2, 0, w^2, 0, 0, w, w, 0, 1, 1, w^2, w^2, 0, 1, w^2, 1, w^2, 1, w^2, w^2, 1, 1, 0, w, 0, 1, 1, w, w, w^2, w^2, 1, 1, w, 0, 0, w^2, w^2, 0, w, 0, w^2, w, w, w^2, 0, w^2, 0, 0, 0, w^2, w^2, w^2, w, 1, w^2, w, w, 1, w^2, w^2, w^2, w^2, 0, w^2, 0, 1, 0, 0, w^2, 0, 1, w^2, 0, w, w, w, w, w, 0, 0, w, w^2, w, w, w, w, w, w^2, 0, w, w^2, 1, 0, 1, w, w^2, 0, 1, w, w^2, 1, w, 0 ] [ 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, w, w, w^2, w^2, 0, 0, 0, 1, 1, w, w, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, w, w, w^2, w^2, 0, 0, w, w, w^2, w^2, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, w, w, w^2, w^2, 0, 0, 1, 1, w, w, w^2, w^2, 0, 0, 1, 1, 1, w^2, 0, 0, w, 0, 0, 1, 1, w, w, w^2, w^2, 1, w, w, w^2, w^2, 0, 1, 1, 1, w, w, w^2, w^2, 0, 0, 1, 1, w, w, 0, 0, 1, 1, w^2, w^2, 1, w, w^2, w^2, 1, w, w, 1, 1, w^2, 1, 1, 1, w, w, w, w^2, w^2, 1, 1, 1, w, w, w^2, w^2, w^2, w^2, w^2, w^2, 1, 1, w, w, w, w, w, w, w^2, w^2, w^2, 1, w, w, w^2, 1, 1, w, 1, w^2, w^2, w, w, w^2, w^2, 1, 1, w, w, w^2, w^2, w^2, w^2, 1, 1, w, w, w, w, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, w, w, w^2, w^2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, w, w, w^2, w^2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, w, w, w, w^2, w^2, w^2, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, 1, 1, 1, 1, w, w, w, w^2, w^2, w^2, 1, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 1, 1, 1, 1, w, w, w, w^2, w^2, w^2, 1, 1, 1, 1, w, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2 ] [ 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 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, 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 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2004-04-21
Lb(180,6) = 130 BKW Ub(180,6) = 132 follows by the Griesmer bound.
Notes
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