lower bound: | 104 |
upper bound: | 105 |
Construction of a linear code [144,6,104] over GF(4): [1]: [144, 6, 104] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w^2, 1, 0, 0, w, w^2, w, w, w^2, 0, w^2, 0, 1, w^2, 1, 1, w, 0, 1, 1, 1, 1, w^2, 0, 1, 0, 1, 1, 1, 0, w, w^2, w, w^2, w, w^2, w, 1, w^2, 1, w, w^2, 1, w, w^2, w^2, 1, w, w^2, 1, w, 1, w^2, w^2, w, 0, 1, w^2, w, 0, w^2, w^2, w, 0, 1, 1, w, w, 1, w, 1, w, 0, 1, w^2, 1, 0, w^2, w^2, 1, 0, 1, 0, w, 0, w, w^2, 0, 0, 0, w^2, 1, w, 1, w, w^2, w, w, w^2, w^2, w^2, w, w, w^2, w^2, w, 0, 0, w, w^2, 0, 0, w^2, w, w^2, w, w, w^2, w^2, 0, 1, 0, 0, 0, 1, w, w, w^2, 0, 0, 0, 0, w, 1, 1, w^2, 0, 0 ] [ 0, 1, 0, 0, 0, 0, w, w^2, w, w, w^2, 1, 0, 0, 1, 0, w, 0, 1, 1, 1, w^2, w, w, 1, 0, 1, 1, 0, w^2, 1, 1, 1, 0, 1, 0, 1, w^2, w^2, w, 1, 1, w, w, 1, w^2, w^2, w, 1, 1, 1, w^2, w, 1, 1, w, 1, w^2, w^2, 0, w, w, w, 0, 1, w^2, w^2, w^2, 1, 1, w, 0, 1, w, w, w, w, 0, 1, w^2, w^2, 0, 1, w^2, 1, w^2, w, 0, w, 0, w, 0, 0, w^2, 0, 0, 1, w^2, w, 1, w^2, w, 1, w^2, 1, w, 1, 1, w^2, 1, w, 1, w^2, 1, 0, 0, 1, w, 0, 0, w^2, 1, 0, 0, w^2, w^2, w, w, w^2, w, 0, 0, w, 1, 0, 1, w^2, 0, w, w^2, 0, 0, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, w^2, 1, w, w, w, w^2, 0, w^2, 0, w^2, w^2, 1, 1, 1, 0, w, 1, 1, w^2, 0, 1, 1, 0, 1, 1, 1, 0, 1, w^2, w, w^2, w, w, 1, w, w^2, w^2, w, 1, w^2, w, 1, w^2, w^2, 1, w, 1, w^2, 1, w, w^2, w^2, 0, w, w^2, 1, 0, w, w^2, w^2, 1, 1, 0, w, w, w, w, 1, w, 1, 1, 0, 1, w^2, w^2, 0, 1, 0, w, w^2, w, 0, w, 0, 0, 0, w^2, 0, w, 1, w^2, w^2, w, 1, w, w, w^2, w^2, w, w^2, w, w, w^2, w^2, w, w^2, 0, 0, w, w^2, 0, 0, w, w^2, w^2, w, 0, 1, 0, w^2, 0, 0, w, 1, 0, 0, w, 0, 0, w^2, 0, 0, w^2, 1, w, 1 ] [ 0, 0, 0, 1, 0, 0, w, w, w, w^2, 0, 0, w^2, 1, 0, 1, 0, w, 1, 1, w^2, 1, w, w, 0, 1, 0, w^2, 1, 1, 1, 1, 0, 1, 0, 1, w, w^2, w^2, 1, w, w, 1, 1, w, w^2, w^2, 1, 1, 1, w^2, 1, w, 1, w, 1, w^2, 1, 0, w^2, w, w, 0, w, w^2, 1, w^2, w^2, 0, w, 1, 1, w, 1, w, w, 0, w, w^2, 1, 0, w^2, w^2, 1, 0, 1, 1, 1, 0, w, 0, w, 0, 0, 0, w^2, w, w^2, 1, w, w^2, 1, w^2, 1, 1, w, 1, 1, 1, 1, 1, 1, 0, 0, w^2, 1, 0, 0, w, 1, 0, 0, w^2, 1, w, w, w^2, w^2, w, w^2, 0, 0, 0, 0, w, w^2, 1, 1, 0, 0, 0, 0, w, w^2 ] [ 0, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, w, w, w^2, w^2, 1, 1, 0, 0, w, w, w^2, w^2, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, w, w, w, w, w^2, w^2, w^2, w^2, 1, 1, 1, 1, w, w, w^2, w^2, 1, 1, 1, 1, 0, 0, w, w, w^2, w^2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, w, w, w^2, w^2, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, w, w, w, w^2, w^2, w^2, w, w, w, w^2, w^2, w^2, 0, 0, 0, 0, w, w, w, w, w^2, w^2, w^2, w^2, 1, 1, 1, 1, 0, 0, 0, 0, w, w, w^2, w^2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2009-05-04
Lb(144,6) = 103 is found by truncation of: Lb(145,6) = 104 Koh Ub(144,6) = 105 follows by a one-step Griesmer bound from: Ub(38,5) = 26 follows by a one-step Griesmer bound from: Ub(11,4) = 6 is found by considering shortening to: Ub(10,3) = 6 GH
Koh: Axel Kohnert, email, 2006.
Notes
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