lower bound: | 172 |
upper bound: | 177 |
Construction of a linear code [244,8,172] over GF(4): [1]: [244, 8, 172] Linear Code over GF(2^2) Code found by Markus Grassl via extension Construction from a stored generator matrix: [ 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, w, 0, 0, 0, w, 0, 0, 0, 0, w, w^2, 0, w^2, 0, w, 0, w, 1, 0, 1, 0, 0, 1, 0, 0, w^2, w, 0, 1, 1, w, w, 0, w, 1, 0, w^2, 0, w^2, 1, w, w, 1, 1, 1, w^2, w, w^2, w, w, w^2, w, w^2, 0, w^2, 0, 1, w, w^2, w, 1, w, w^2, 0, w^2, 0, w^2, w, 1, 0, 1, 0, w^2, 0, 0, 1, w^2, w, 1, w, 0, 0, 1, 1, w^2, 0, 1, w^2, w^2, w, 0, w, w^2, 0, w^2, w, w^2, 1, w^2, 1, w, w, w, 1, 0, 0, w, w, 1, 1, 1, 0, w^2, 0, w, 0, w, 1, w^2, w, 1, w^2, 0, w, w, w, 1, 1, 0, w, 1, w, 1, w, w^2, 0, w^2, 0, w^2, w, w^2, w, 1, 0, 0, w, w^2, w, w, w, 0, w^2, 1, 1, 0, w^2, w, 1, 1, 0, w^2, 1, 1, 0, 1, w^2, w, 0, w^2, w^2, w, 0, w, w^2, w, 1, w^2, w, 1, 0, 0, 0, 1, 0, w, 1, 1, w^2, 1, w, 0, w, w^2, 0, w, 1, w, w, w^2, 0, w^2, w^2, w^2, 1, w^2, 0, w^2, w^2, 1, 1, w^2, 0, 0, 1, 0, w^2, w, w^2, w^2, 1, 0, 0, w, 0, w^2, 0, w, w^2, 1, 1, w^2, 1, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, w^2, 0, 0, 0, w, 0, 1, 0, w^2, w^2, 1, w^2, w^2, w^2, w^2, w^2, w, w, w^2, w, w, 0, w, w^2, w, w^2, w^2, w^2, 1, w, 1, 0, w, 1, 1, w^2, w, w^2, 1, 1, w, 1, 0, 1, w, w, w^2, w, w, 0, w^2, w^2, w^2, w^2, 0, w^2, 0, 1, 0, w, 1, w^2, 1, w^2, 1, w^2, 0, w, w^2, w^2, 0, w, 1, 1, w^2, 1, 0, w^2, 1, w, 1, 0, w, 0, w^2, 1, 0, 1, w, 1, w, 0, w^2, w, w, 1, w^2, 1, 0, w, 0, w^2, 0, w^2, 0, w, 1, 1, 1, w, 1, w, 0, w^2, w, w^2, w^2, 0, w, 0, 0, w^2, 1, 1, 0, 1, 1, w, w^2, w, w, 0, w, w, 0, 1, 0, w, w, w, 0, w, w^2, w, w^2, 0, w, w, 0, w^2, 0, w^2, 1, w, w, 1, 0, w, 1, w, 0, w^2, w^2, 1, 0, 0, 1, w^2, 1, 1, 0, w, 1, 0, 1, 0, 1, w, 0, w, 0, 1, 0, 1, w^2, w, 0, 1, w^2, 1, 0, w^2, w, 0, 0, w^2, w^2, w^2, w, 0, w^2, 0, w, w^2, 1, w^2, w^2, 1, w, 0, 1, w^2, w^2, w, 1, 0, 0, 1, 1, w^2, 0, 0, w^2, w^2, w^2, 1, 0, 1, w^2, 0, w, w^2, w^2, w^2, 1, 1, 1 ] [ 0, 0, 1, 0, w, 0, 0, 0, 0, 0, w^2, w, w^2, w^2, 0, w, 0, w^2, w^2, w^2, w^2, w, 1, w, w, 0, w^2, w, 0, w^2, 0, 1, 0, 1, w, w, 1, w^2, 1, 0, w^2, w^2, 1, 0, w^2, w^2, 1, w, 1, 1, 1, w, w^2, w, w, w, w, w, w, w, w, w^2, 1, w^2, w^2, w^2, w^2, 0, 0, w, w, w^2, w, w, w^2, 0, w, 0, w, 0, 0, w, w^2, 0, w, w, w, 0, w, w^2, 0, w, w, 0, 0, w, 0, w^2, 0, 1, w^2, w^2, 0, 0, 0, w, 1, 1, w, 0, 1, w^2, w, w, 0, 1, 1, 0, 0, 1, 1, w^2, 1, w^2, 1, w^2, w^2, w, 1, 1, w^2, 1, 1, 0, 1, w^2, 1, w^2, w^2, 1, w^2, 0, 1, 0, 1, w^2, w^2, 1, 1, 0, w, 1, 0, 0, 0, w^2, w^2, 1, w, 1, w, w, w, w^2, w^2, 0, 0, 1, w^2, 1, 0, w, w, 0, 1, w^2, w^2, 1, 0, w, 1, 1, w, w, 0, 1, 0, 0, 1, 0, 1, w^2, w^2, w^2, 0, w^2, w^2, 0, 0, w^2, w, 0, w, w^2, w^2, w^2, w, w, w^2, w, 1, 1, 1, w, w^2, w^2, w^2, w, 1, 1, 0, 1, w, w, w, w, w^2, 1, 1, 1, w^2, 0, w, w, w^2, 0, w^2, 0, 1, 1, 0, 0, 0, 0 ] [ 0, 0, 0, 1, w^2, 0, 0, 0, 0, 0, 0, w, 1, w^2, 1, w, 0, w^2, w^2, w^2, 0, w, w^2, w, w, 0, 0, 0, 0, w, 1, w, 0, 0, w^2, w, 0, w^2, 0, 1, 0, 1, w, w, 1, w^2, w, w^2, 0, 1, 1, 1, 1, w^2, w, 0, w^2, 0, w, 1, w, w^2, w, w, 1, 1, w, 1, 1, 1, w, 1, 1, w^2, 0, w, 0, 1, w, w^2, w, 1, w, 0, w, w, w^2, w, 0, w^2, w, 1, w, 0, 1, 1, w, 0, 1, 1, w^2, w, 1, w^2, 0, 0, w^2, w^2, w^2, 1, 1, w, 0, w, w, 0, 0, w, 1, w, w, w^2, 0, 1, 1, 0, w^2, 1, w^2, w^2, 1, w, w^2, w, w, 0, 0, 0, w, 1, w, w, 1, 0, 0, 1, 1, w^2, 1, w^2, 0, w, 0, w^2, 1, 0, 1, w^2, 0, w^2, w^2, 0, w^2, w^2, 1, 0, w^2, 0, w^2, w, 1, 1, w, w^2, w^2, w^2, w, 1, 1, 1, w^2, 1, 0, w^2, w, w^2, w, w^2, 1, w^2, 1, w, w^2, 1, 0, w, w, w^2, w, w^2, 1, 0, w^2, w, w, 0, w, 1, 1, w^2, w^2, 1, w, w, w, 1, w^2, w, w^2, w, w^2, w^2, w^2, w^2, 0, 1, 0, 0, w^2, 1, w^2, 1, 0, w, 1, w, 1, 1, w^2, 1, w, w^2, w^2, w^2 ] [ 0, 0, 0, 0, 0, 1, 0, w, 0, 0, 0, w, 0, w^2, 0, 1, w, w, w^2, w^2, w^2, w, w^2, 1, w, 0, w, w, w, w, 0, 0, w^2, w^2, 0, 0, 1, 1, 0, 1, 1, 0, 0, w^2, 1, w^2, w^2, 1, w, w^2, 1, 0, w^2, w, w^2, w, w^2, w, w^2, 1, w^2, 1, w^2, w^2, w, w, w^2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, w, w, 0, w, w, 1, 0, 0, w^2, w^2, w^2, w^2, 1, 1, 1, w, 1, w^2, w, 1, w, 0, w, 1, w, w^2, w, w^2, w, w^2, 1, 1, 0, 0, 0, w^2, w^2, w, w, w^2, 1, w^2, 0, 1, w, w^2, w, w^2, w, 1, w, 0, w, w^2, 0, w, w^2, 0, w, w^2, w^2, 1, 1, w, 1, 0, w, 0, w^2, 0, 0, w^2, 0, 0, w, 0, w, w^2, 0, 0, 0, 1, w^2, 1, w, 0, 0, 0, 0, 1, w, w, 1, w, 1, w^2, 0, 1, 1, w, 1, 0, w^2, 0, 1, w, 0, 0, 1, w, w^2, 0, w, w, 1, w^2, w, w^2, 0, 1, w^2, w, 0, 1, w, 0, w, w, 0, w, w^2, 1, w^2, 1, w^2, w, w, 1, w, 0, w^2, 1, 0, 1, w^2, 1, 0, 0, 0, w, w, w^2, w, 1, w, w^2, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, w, w, w, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, w, 1, 1, 1, 1, 1, 1, w^2, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, w, 1, 1, 0, w, w, 0, 0, 1, 0, 1, w, 0, w, w, 0, w, w, 1, 0, 0, 1, w, w, w^2, w^2, 0, 1, 0, w, 1, w, 0, 1, 1, w^2, w^2, 1, w, 1, 0, w^2, w, 0, w, w, 0, 1, 0, 0, w, 1, w^2, 1, 1, w, w, w^2, 0, 1, 1, w, w^2, w^2, w, 0, 1, 0, w^2, 0, w, 0, w^2, 0, 1, 1, w, w^2, w^2, w, w^2, w^2, w, w, 1, 0, 0, w^2, w, w^2, w^2, w, w, 0, 0, w, w, w^2, w^2, 0, 0, w, w^2, w^2, 0, w, w^2, w^2, 0, 1, w, w, 1, 0, 1, 1, w^2, w, w, 1, 1, 1, 0, 1, w^2, 0, w, 0, w, 0, w^2, 0, w^2, w, 1, w^2, w^2, w, 1, w^2, w^2, w^2, w^2, 0, w, w, 0, w^2, 1, 1, w, 0, 1, 0, 1, w^2, 0, w^2, 1, w, 0, 1, 0, w, 1, w^2, w, w, 1, 0, 0, 0, 0, w^2, w^2, w^2, w, 0, 0, w^2, w, w^2, w^2, w, w^2, 0, 1, w^2, 0, w^2, w, w^2, 1, w^2, 1, 1, w^2, 0, w, 1, 0, w^2, w^2, 1, 1, w^2, 0, 0, 0, w^2, w, 1, w, w, 1, 0, 1, 1, w^2, w^2, w, 0, 0, w, w, 1, w^2, 1, w, w, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, w^2, 0, 0, 1, w^2, w^2, 1, 1, 0, 1, 0, w^2, 1, w^2, w^2, 1, w^2, w, 1, 0, 0, 1, w, w, w, w, 1, 0, 1, w^2, 0, w^2, 1, 0, 0, w, w, 0, w^2, 0, 1, w, w^2, 1, w^2, w^2, 1, 1, 0, 0, w, 1, w^2, 1, 0, w^2, w^2, w, 1, 0, 0, w^2, w, w, w^2, 1, 0, 1, w, 1, w^2, 1, w, 1, 0, 0, w^2, w^2, w^2, w, w^2, w^2, w, w, 1, 1, 1, w, w^2, w, w, w^2, w^2, 1, 1, w^2, w^2, w, w, 1, 1, w^2, w, w, 1, w^2, w, w^2, 0, 1, w, w, 1, 0, 1, 0, w, w^2, w^2, 0, 0, 0, 1, 0, w, 1, w^2, 1, w^2, 1, w, 1, w, w^2, 0, w, w, w^2, 0, w, w, w, w, 1, w^2, w^2, 1, w, 0, 0, w^2, 1, 0, 1, 0, w, 1, w, 0, w^2, 1, 0, 1, w^2, 0, w, w^2, w, 1, 0, 0, 0, 0, w^2, w, w, w^2, 1, 1, w, w^2, w, w, w^2, w, 1, 0, w, 1, w, w^2, w, 0, w, 0, 0, w, 0, w, 1, 0, w^2, w^2, 1, 0, w, 1, 1, 1, w, w^2, 0, w^2, w^2, 0, 1, 0, 0, w, w, w^2, 1, 1, w^2, w^2, 0, w, 0, 0, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2008-09-06
Lb(244,8) = 168 is found by shortening of: Lb(245,9) = 168 is found by truncation of: Lb(248,9) = 171 is found by construction B: [delete from a [256,16,171]-code the (at most) 8 coordinates of a word in the dual] Ub(244,8) = 177 is found by considering truncation to: Ub(241,8) = 174 DM4
Notes
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