lower bound: | 150 |
upper bound: | 158 |
Construction of a linear code [220,9,150] over GF(4): [1]: [222, 9, 152] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, 0, w^2, 0, w, w, w, w, w, 1, w^2, 1, w^2, 0, 0, 0, w^2, 1, 1, w^2, 0, w, 1, 1, w, 0, w, w^2, 0, 0, 0, w, w^2, w^2, 1, 0, w, 0, 1, 0, w^2, w^2, 0, w^2, 0, w, w^2, 0, 1, w, w, 0, w^2, 0, 0, w, w, w, w^2, w, w^2, w, 0, 0, 1, w^2, w^2, w^2, 0, w, 1, w^2, 1, w, w, 0, w, 1, 0, 1, w^2, w, 0, w^2, 0, 1, w^2, 0, w, w, 1, w^2, 0, 0, 1, 1, 1, w^2, w, w^2, 1, w^2, w^2, 0, w^2, 1, w, 1, w^2, w, w, 0, 1, w^2, 1, 1, w^2, w^2, 0, 0, w^2, w, w, w, 1, w^2, 1, w, 1, 1, 1, 0, w^2, 1, w^2, 0, 0, 0, 1, 1, 1, 1, w^2, 0, w, 1, 0, 0, w^2, w^2, w, 0, w^2, w^2, w, 0, w^2, w, w^2, 1, w, 1, 1, 0, 0, w^2, w^2, w^2, w^2, w, w^2, 1, w^2, 0, 0, w, 1, w^2, 1, 0, 1, w, 1, w, w^2, w^2, w^2, 1, 0, 0, 0, 1, w, w^2, w^2, 1, w, 0, w, w^2, 1, w^2, 1, w^2, w, 0, 1, 1, 1, w^2, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, w, w^2, 0, 0, w, w^2, 0, w, 0, w, w^2, w, w^2, w, w, w, 1, 1, w^2, w, 1, 0, w^2, 1, 0, w, 0, w, 0, w^2, 0, w^2, w, w^2, 1, w^2, 1, 0, 1, w^2, 1, w^2, w, 0, 1, 0, 0, 0, 0, 0, w^2, 0, w^2, w, 0, w, w^2, w, 1, 1, w, w, w, w^2, 1, 0, 0, w^2, w^2, w, 0, 1, 0, w^2, w^2, w, w, 1, w^2, w, w, 0, w^2, w, w^2, w^2, 0, 1, w^2, 1, w, 0, 0, 1, 0, w, 0, w, w^2, 1, 1, w^2, w^2, w^2, w, w^2, 0, w, 0, w^2, w^2, w^2, w, 0, w^2, w, 0, 1, w, w^2, 1, w, w, 0, 0, 1, w^2, 1, 1, w, 1, 1, w^2, w^2, 0, 0, 0, w, w, 1, 0, 0, 1, 1, 1, w, 0, 0, w, w^2, 1, 0, w^2, w^2, w, w^2, w, 0, 0, w^2, w^2, 0, 1, 0, 0, 0, w^2, 0, w, 0, 0, 1, 1, 0, w, 1, w^2, w, 0, w^2, 1, w, 0, w, 0, 1, 0, w^2, 1, w, w, w^2, 0, w, 0, w^2, 0, 1, 0, 1, w, 1, w^2, w, w, 1, w^2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, w, 0, w, 0, 0, w^2, 1, 0, 0, 0, w, w^2, w^2, 0, w^2, w, 1, 0, 0, w, w, 0, w^2, w, w, w^2, w, w, 0, w, 1, w^2, w, 1, 0, 1, w, w^2, w^2, 1, w^2, 1, 1, w, 0, w, w, w^2, 0, w^2, w, 1, 0, w, w, w^2, 1, 0, 0, 0, 1, w^2, 1, 1, 0, 1, 0, 1, 0, w, w^2, 0, 0, w, w, 1, 0, w, 1, w^2, 1, 1, 1, 1, 0, w, w^2, w, 0, w, 0, 0, 1, 0, 0, 1, w, w^2, 0, w, w^2, 0, w, 1, 0, 0, w^2, 1, w, w, 1, 0, w^2, w^2, 0, 1, w, 0, 0, 1, w^2, 1, w, w, w, w, 0, w, w, 1, 1, w, w, w, w^2, 1, 0, 1, w, w^2, w^2, 0, 1, 1, w^2, w^2, w, 1, 1, w^2, 0, 1, 1, w, 0, 0, 0, 0, 1, w, w, w^2, w, w^2, 1, w, w^2, 1, 0, 0, 1, w^2, 1, 1, w, w^2, w^2, 0, w^2, 0, 0, 1, w, 1, w, 1, w, w, 0, 1, w, w, w^2, 0, 1, 0, 0, 0, w, 1, w, w, w, 0, 0, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, w, w, w^2, 0, 0, 0, w^2, w, 1, 1, w^2, w, w, w, 1, 0, w, 1, w^2, w^2, w^2, 0, 1, 0, 1, 1, 1, w, 0, 0, 1, 0, 0, w^2, 0, 1, 0, w^2, w, w^2, 1, 0, w^2, w^2, w^2, w, 0, 1, w^2, w, w^2, 0, w, 0, 1, w^2, 0, w, 1, 1, w^2, w, 1, 0, 0, w, 0, w^2, 1, 1, 1, 0, w^2, w, 0, 0, w^2, w, 0, 1, 1, 1, w, w, w^2, w, w, w, 0, w, 1, 0, w, 0, 0, w, w, w^2, w, w^2, w^2, w, 1, w^2, 1, w, w, w^2, w^2, w^2, 0, 0, 1, 0, w^2, w, w^2, 0, 0, w, w, 1, 1, 0, w, 1, w^2, w, 1, w, 1, 1, 1, 1, 0, 0, w, 0, w^2, 0, 0, 1, w^2, w, 1, 1, w^2, w^2, w, w^2, w^2, 1, 0, w^2, 1, 1, w^2, 0, 1, 0, w, 1, 0, 1, 1, w^2, 0, 1, 0, w^2, w^2, 1, w^2, 0, w^2, w, w^2, 1, w^2, 0, 1, w, 0, w, 0, w, w^2, w, w^2, w, w^2, w, 0, 0, w^2, w^2, 1, 1, 0, w, w^2, w, w, 0, w^2, 0, w, 0, 0, 0, 0, 0, w, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, w, 1, w^2, 0, 0, 1, 0, w, w^2, 1, 1, 0, w, w, w, w^2, w^2, 1, w^2, w^2, w, 0, w, 1, w, 0, 0, w^2, 0, 1, 0, w^2, 0, 1, 0, 0, w, 0, w^2, 1, w, 1, w^2, 0, 0, w, w^2, 1, w^2, 1, w, w, 0, w^2, 0, 1, w^2, w^2, 0, w, w^2, 1, w, w, 0, 0, 1, w^2, 1, 0, 0, w^2, 0, w^2, 1, w, w, 1, w^2, w, 1, w, w^2, 0, w^2, 0, w^2, 0, w, w^2, w^2, w^2, w^2, 0, w^2, w, 0, w^2, w, w^2, w^2, w, 1, w^2, 1, w, w, 0, 0, 1, 1, 1, 0, w^2, w^2, w, w, 1, 0, w^2, 0, 1, w, w^2, w^2, w, w^2, w, w, 1, w^2, w, 0, 0, 1, w^2, 0, 1, w, 0, 0, w^2, 0, 0, w, 1, w^2, w, 0, w, 1, w, 1, 0, 1, w^2, w, w, w, 1, 0, w, 1, w, 1, 0, w, w, w, 0, w^2, w^2, 0, 1, w, w, 1, w^2, 1, 0, w^2, 0, 0, w^2, w^2, 0, 1, w^2, 0, w, 0, 0, w, w^2, w^2, w^2, w^2, w, w, 0, w, w, 1, w^2, 1, 1, 1, 0, 0, 0, 0, 0, w, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, w^2, 0, w^2, 0, 0, w^2, w, 1, 1, 0, w^2, 0, w, 0, w, w, 0, w, 1, w, 1, 1, 1, 0, w^2, 0, 1, 1, w, w^2, w, w, 1, w^2, w, w^2, 0, 1, w^2, w, 1, w, 1, 1, 0, w, w^2, 0, w, w^2, w^2, w^2, w, 0, 0, w, 0, w^2, w, w, 0, w, w^2, 1, w^2, 0, 0, 1, w^2, 1, 0, w^2, w, 1, 1, 1, 1, 1, w, w, w, 1, w, w^2, w, w^2, 1, w, w^2, w^2, 1, 0, w^2, 1, 0, w^2, w^2, w^2, w^2, 0, 1, w, 1, 0, 1, 1, w^2, w, 1, 0, 0, 1, 0, w, w^2, w, w^2, 1, 1, w^2, w, 1, 1, 1, w, 1, w, w^2, 1, 1, 0, w, 0, 1, 1, 1, w^2, 1, w^2, w^2, w, 1, w, w, 0, w, 1, 0, w^2, w, 1, 1, w^2, w, 1, w^2, 0, w^2, 0, w^2, w^2, 1, w^2, w^2, w, 1, w, w^2, 1, 1, 1, 0, w^2, w^2, w, w, 0, 0, w^2, 1, w, w^2, w^2, 1, 0, 1, 1, 0, 0, 1, w, w^2, 0, 0, 0, 1, 0, w, w, w^2, 0, 0, 1, 0, w, w^2, w^2, 0, w, w^2, 1, 1, w, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, w, 0, 0, w^2, 0, w^2, w^2, w, w^2, 1, w^2, w^2, 0, w^2, w^2, w^2, w^2, w, w, w, w^2, 0, w^2, w^2, 0, w^2, w, w^2, w, 1, 1, 1, w^2, w^2, 1, 0, 0, 0, w^2, w, w^2, 1, 0, w^2, w, w^2, 0, w^2, w^2, w, w, 1, 1, 0, w, 0, 0, w, w, w^2, w, 0, 1, 1, 0, w, w, 0, 1, w^2, w^2, 0, w, w, w, w, 1, 1, 0, 0, 0, w^2, 0, 0, 1, 1, w^2, w, w^2, 1, w^2, 0, 1, 1, w, w^2, w^2, 0, 0, 1, w^2, w^2, 1, 0, w, w^2, 0, w^2, w^2, w, w^2, 0, 0, 0, w, w^2, 0, w^2, 0, 1, w^2, 1, 0, w^2, 1, 0, 0, 1, w^2, 1, w, 0, 1, 0, 0, 0, w, 1, 0, w, w, w, 0, 0, 0, w, w^2, w^2, 0, 0, 1, 1, w, 0, 0, 1, 1, 1, w, 1, w^2, w, 1, w, 1, w^2, w, w^2, 0, w, w, w^2, w, 0, w, 1, w, w, w^2, 1, 0, 0, 1, w, w^2, w, 0, w^2, 0, w^2, 1, w^2, w, 1, 0, w^2, w, 1, w^2, w^2, 1, 0, w, 1, 0, w, 0, 0, 0, 0, 0, 0, w, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, w, 0, 1, w, 0, 1, 1, 1, 1, 0, 1, 1, w, w^2, 1, 1, 1, 0, 1, w, 1, 0, 0, w^2, 1, w^2, 1, w^2, w^2, 0, 0, w^2, 1, w, w, w, w^2, 0, w, 0, 1, w^2, w^2, w, w, w^2, 0, w, w, 0, w^2, 0, 1, 1, 0, 1, 1, 0, w^2, 0, w, w, 1, w^2, w, w^2, w, w, w^2, w^2, w, 1, 0, 0, w, 1, w, 1, 1, 0, 1, w, w^2, 0, w^2, 1, w, w^2, 1, 0, 0, w, 0, 1, 0, w^2, 1, 0, 0, w, 1, 1, w, 0, w^2, 1, 0, 1, w^2, w, w^2, 1, 1, 0, w, w^2, 1, w^2, 1, 1, 1, w^2, 1, w^2, w, 1, w^2, w^2, w^2, w, w, w^2, 0, 0, 1, w^2, 0, 1, 1, 1, 0, 1, w^2, w^2, w^2, 0, 0, 1, w^2, 0, 1, w, 0, w, w, w^2, 1, w, w^2, 0, w^2, w, 0, 0, 1, w^2, w^2, w^2, w, w^2, 0, w, w^2, 1, 1, 0, w, 1, 1, 1, 0, w, w^2, 1, 1, w, 0, 0, w, w, 1, w, w, 0, 1, w^2, w^2, w^2, 1, w, 1, 1, 1, w^2, w, 1, w^2, 0, 0, 0, 0, 0, w^2, w ] [ 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, 1, 1, 1, 0, 0, 1, 1, 1, 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, 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, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 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, 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, 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, 0, 0, 0, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [220, 9, 150] Linear Code over GF(2^2) Puncturing of [1] at { 221 .. 222 } last modified: 2012-08-21
Lb(220,9) = 148 is found by truncation of: Lb(224,9) = 152 MST Ub(220,9) = 158 is found by considering shortening to: Ub(219,8) = 158 is found by considering truncation to: Ub(217,8) = 156 DM4
MST: T. Maruta, M. Shinohara & M. Takenaka, Constructing linear codes from some orbits of projectivities, to appear in Discr. Math.
Notes
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