lower bound: | 106 |
upper bound: | 110 |
Construction of a linear code [152,7,106] over GF(4): [1]: [152, 7, 106] 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, w, w^2, w, 0, 1, 1, 1, w, w^2, w, w, 1, w, 1, w^2, w^2, w, w, 0, w^2, w, w^2, 0, 1, 1, w, 1, w^2, w^2, 0, w^2, w, 0, w, 0, 1, w, 1, 0, 0, 0, 1, w^2, w, w, 0, 1, 0, w^2, 0, w, 0, 1, 1, 1, 0, w, w, w, 1, w, w^2, w^2, w^2, 0, 1, w, w, 0, 0, 0, 0, w^2, w, w^2, w^2, w, w^2, w, w, w, 0, w^2, w, 0, 0, 1, w, 0, 0, 0, 0, w^2, 1, w, 0, 1, 1, 0, w^2, w^2, 0, w, 1, w^2, 0, w^2, 1, w, 1, w^2, 1, w, 0, w^2, 0, w, 1, w, 0, 1, w^2, w^2, w, 0, 0, 0, 0, 1, 0, 1, 0, w^2, w, w^2, 1, w, w, 1, w, 0, w, 1, 0, w^2, w ] [ 0, 1, 0, 0, 0, 0, w, w, w^2, 0, 1, w^2, 1, 1, 0, w, 0, 0, 0, 1, 0, w^2, 1, w, 1, w, 0, w^2, w^2, w, 1, 0, w, w^2, 1, 1, w, 0, w, w, w, 0, 1, 0, w^2, w, w^2, 1, w^2, w, 0, w^2, 1, 1, w, w^2, 0, 1, 0, 1, w, 1, 0, 1, w^2, w^2, w^2, w, 0, 1, 1, 0, 1, 1, 1, w, w, 0, 1, w, w, w, w^2, 1, w, w, w^2, 0, 0, w, w^2, w^2, w, 0, 1, w, 1, 1, w, w^2, 1, w^2, w^2, 1, w^2, w, w, w, w^2, w, 1, w^2, w, 1, 1, 0, w^2, w^2, w, 1, 0, 1, w, 0, 1, w, w^2, w^2, 1, 0, 0, w, w, w, 0, 1, 0, 0, w, w^2, w^2, 0, 1, 1, w^2, 1, 0, w, 0, w^2, w, 0 ] [ 0, 0, 1, 0, 0, 0, w^2, w, w, 0, 0, w, 1, w, w, w, 0, w^2, 0, w, 1, 1, w, 1, 1, 1, w, w^2, 0, 0, 0, w, w^2, w^2, 1, w, w^2, 0, 0, 1, w^2, 0, w, 0, w, 0, 1, w, w^2, w^2, 1, w^2, 0, 1, 0, w, w^2, 1, 1, 0, 0, w, 1, w^2, 1, w, 0, 0, w, 0, w^2, w^2, 1, 1, w^2, w^2, w^2, 1, w, 0, 1, w, w, 1, 0, 0, 1, w^2, 0, w^2, 1, 1, 1, w^2, 0, w^2, 0, 0, 0, 0, 1, 1, 1, w^2, 0, 1, 1, w, w^2, 1, 0, 1, w^2, w, 1, w^2, w, w, 0, 1, w, 0, 1, w^2, 1, 0, w^2, 1, w^2, 0, w, 0, 1, 1, w, 0, 0, 1, w^2, w^2, w, w, 0, 0, w, w^2, 0, w, w, w, 0, w^2 ] [ 0, 0, 0, 1, 0, 0, w^2, w^2, w, 0, 1, 1, w, 0, w, 0, w^2, w, w, w, w^2, w, 1, w^2, w, w^2, w, w^2, w, 1, 1, w, w^2, 0, 0, w, w, w, 0, w, 0, 0, w^2, 1, 0, w, 1, w^2, 0, w, w, 0, 1, w^2, 1, 1, 0, w, 0, w^2, w^2, 1, 0, 0, w^2, w, w, w^2, w^2, 0, w, 0, w^2, w^2, w^2, w, 1, 1, w^2, w, 0, w, 0, w, 0, 1, 1, 1, 0, 1, 0, w, 1, 1, 1, w^2, w, 1, 1, w, 0, w, 1, 1, 1, 1, 1, w^2, 1, w, 0, w^2, 0, w, w^2, 0, w, 1, w, 0, w^2, 0, w, 1, w, 0, 0, 0, 1, w^2, 1, 1, 1, w^2, w^2, 1, w, w, w, w^2, w, 0, 1, 0, 0, 1, w, w^2, 1, w, 0, w^2 ] [ 0, 0, 0, 0, 1, 0, w, w^2, w^2, 0, w^2, 0, w^2, w, 0, w^2, 1, 1, 1, 0, w, 0, 0, w^2, 0, w^2, w^2, w^2, w^2, 0, w, 1, w^2, w^2, 0, 0, w^2, 1, w, 0, 1, w, 0, 0, w, 0, w, 0, w, 0, 1, 0, 1, w, 0, 1, 1, w^2, w, 0, 0, w^2, 1, 0, w, w, w^2, 0, w^2, w^2, w, 0, w^2, 1, 1, w^2, 0, 1, 1, 1, w, 1, w^2, 1, 0, 1, 1, 1, 1, 1, 1, 1, w, 0, w^2, 0, w, w, w, w, 0, w^2, 0, w^2, 0, 0, 1, 1, w, w^2, 0, 0, 1, w, w, w^2, 0, w, w^2, 0, 1, 0, w^2, 1, 0, w^2, 0, 1, 0, 1, 1, w^2, 1, w, w, w, w, 1, w^2, w, w, w^2, 1, w^2, 0, w^2, 1, w^2, 1, 0, w^2, w ] [ 0, 0, 0, 0, 0, 1, w^2, w, w^2, 0, w, 1, 0, w^2, w^2, 1, 0, 1, w, w^2, 0, 0, w^2, w, 1, w^2, w, 0, 1, 1, 1, 1, w, w, 1, w^2, 1, w^2, w, 1, w, 1, w^2, 1, w, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, w^2, w, 1, 0, w^2, 0, 1, 0, 0, w, 1, 1, w, w, 1, w^2, w^2, w^2, w^2, w, 1, 0, 1, w^2, w^2, w^2, w, w, w, 1, 0, 1, 1, w^2, w^2, w, 1, 0, 0, w^2, w^2, w^2, w^2, w, w^2, 0, w^2, 0, 1, w^2, 0, w, w^2, 0, w, w^2, w, 0, 1, w^2, 1, 0, w^2, 1, 0, w, 0, 1, 1, 0, 0, 1, w^2, 1, w^2, w, w, w, 1, w, w, w, w^2, 0, w^2, 0, 0, w, w^2, w^2, w^2, w^2, w, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2007-09-28
Lb(152,7) = 105 is found by truncation of: Lb(155,7) = 108 Koh Ub(152,7) = 110 follows by a one-step Griesmer bound from: Ub(41,6) = 27 Da
Koh: Axel Kohnert, email, 2006.
Notes
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