lower bound: | 148 |
upper bound: | 155 |
Construction of a linear code [216,9,148] over GF(4): [1]: [216, 9, 148] 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^2, w, w, 0, w^2, w^2, 1, w^2, w^2, w, 1, 1, w^2, w, w^2, w^2, 0, 1, 1, w^2, w^2, w^2, 0, w^2, w, w^2, 0, 1, w^2, 0, w^2, w, 0, w, w, 0, 1, 1, 1, 1, w^2, w, w, 1, w, 1, 0, w, w, 0, w, 1, w, 1, w^2, w^2, 0, 0, 1, w, 0, 1, w^2, 0, w^2, 1, 0, 1, w, w^2, w^2, 0, 0, w^2, 0, w^2, 1, 0, w, w, w^2, 1, w, w^2, 1, 1, w, w, 0, 1, w, w, w, w^2, w^2, w^2, w^2, 0, w^2, 0, w, w^2, 0, w, 1, w^2, 1, w^2, 1, w, 1, 1, 1, 0, w^2, w, 0, 0, w^2, 0, w^2, w, w, 0, w^2, 1, w^2, w, w^2, w^2, 1, w, 1, w^2, 0, w^2, w, 1, w^2, 0, 0, w, w, 0, w, w, 0, 0, w, w^2, 0, 1, w, w, 1, w^2, w^2, w^2, 0, 1, 1, 1, w, w, w, w^2, w, 0, w^2, 0, w^2, w^2, w, w^2, 1, w^2, 0, w, 0, 1, 0, 1, 0, w^2, 1, 0, 1, w, w, 0, 0, w, 0, w^2, w^2, 1, w, 0, w^2, w^2, w^2, 0, 0, 0, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, w^2, 0, w, 1, w, w, 1, 1, 1, 1, 0, 1, w^2, w, 0, 0, w, w, 1, 1, 0, 1, w, 0, w^2, 0, w^2, w^2, 0, 0, 1, 0, w, 0, 1, w^2, w, w, w^2, 0, w, w^2, w^2, 0, w, w^2, 0, w, w, w, w^2, 0, 0, w, w^2, 1, 0, 0, 1, w^2, w^2, 1, 1, w, 0, 1, 1, 1, 0, w^2, w, 0, 1, w, w, w^2, w^2, 1, 1, w, w, w^2, 0, w^2, 1, 1, w^2, w, w^2, w^2, 0, 1, 1, 1, 0, 0, 1, w, 0, w^2, w, w, w, w^2, w, w, w^2, w^2, w^2, 1, w, 0, w, 1, w, 1, w, 1, w^2, w, w^2, 0, 0, 0, 1, 0, w^2, w^2, w^2, 0, w^2, w, w, w^2, 1, 1, w, w, w^2, w^2, 0, 0, w, 1, 1, 0, w, w, 0, w^2, 1, w^2, w, w^2, 0, 1, w^2, 0, w, w, w, w^2, w^2, w, 0, w, w^2, w^2, 1, w^2, w^2, w, 1, 0, w^2, w, w, w, w^2, 0, 1, 0, w, w, w^2, 0, w, 0, w, w, 0, 0, 0, w, 1, w, w, 0, w, 0, 0, 0, w^2, 0, 1, w, w^2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, 1, w, 1, w, 0, w, w, w, w^2, w, 0, w^2, 0, w, w, 1, w, w, w^2, 0, 0, w^2, w^2, w^2, w^2, w^2, 1, w^2, 1, 0, 0, 1, w^2, 0, w^2, w^2, 0, 1, 0, 0, w^2, 1, w, w^2, w, 0, 0, 1, w, 1, 0, w, 1, 0, w, w, w^2, w, w, w^2, 1, w, 1, w^2, 1, 0, w, 1, w^2, w^2, w^2, 0, w^2, w, 1, w, w, w^2, 0, 0, 1, w, w^2, w^2, 1, w^2, 1, 0, w, 0, 1, 1, w, w^2, 1, 1, 0, w^2, w, 1, w^2, w, w^2, w, 0, 0, 0, w^2, 1, 0, w^2, 0, w^2, w^2, w, w^2, 0, 0, w^2, 0, w^2, w^2, 0, w^2, w, 1, w, 0, w^2, w^2, 1, w^2, 0, w^2, w, w^2, 0, w, w, 1, 1, w^2, 0, 1, 1, 0, 0, w, w, w^2, w^2, w^2, 1, w, 1, w, w^2, 1, w^2, 1, w^2, w, 0, w^2, 1, w^2, w^2, 1, w^2, w, 0, 1, 1, 0, 1, w^2, w, 0, w^2, w^2, w, w^2, 1, 0, w^2, w, w^2, w, w^2, 0, w^2, 0, w, 1, w^2, 1, 1, w, 1, w, 0, w^2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, w, w^2, w^2, w, w, 1, 1, w, w, 0, w^2, w^2, w, w, 0, w^2, 1, w, 1, w, w, w, 1, w, 0, 0, w, w^2, 1, w^2, w^2, 1, w, 1, w^2, w^2, w^2, w, 1, 0, 0, 1, w^2, 1, 0, 1, w^2, w, w, 1, w^2, w, 1, w, w^2, w^2, 1, w, w^2, w^2, 0, w^2, 0, 1, w^2, 1, 0, 0, 0, w^2, w^2, w, w^2, 0, 1, w^2, w, 1, 1, 1, w, w^2, w, w^2, 1, 1, 0, 1, w^2, 0, w^2, 1, w, w, w, 1, 1, 0, w, w, w^2, 0, 0, 0, 1, 0, 0, w, 1, 1, w^2, 1, w^2, 1, 0, w^2, 1, 0, 0, w, w, 0, 1, w, w, 0, w^2, w^2, 0, w^2, w, w^2, w, 0, w, 1, w^2, 1, w^2, w^2, w, 0, 1, w, w, w, 0, 0, w^2, 0, w^2, 1, 1, w^2, 0, 1, 1, 0, w, w^2, 0, w^2, w, 1, w^2, w^2, w^2, w, 0, w, 0, w^2, 1, w, 0, w^2, 1, w, w^2, w^2, w, 1, 0, 1, 1, w, 0, w, 1, 1, w^2, 0, 0, 1, 1, w^2, w^2, w^2, w^2, w^2, w, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, w^2, w^2, 0, 1, w^2, w, w^2, 1, 1, 1, w^2, w^2, 1, 0, w, w^2, w^2, 1, 1, 1, 1, w^2, w^2, w, 0, w^2, 1, w^2, 1, 1, w^2, w, 0, 1, w, w, w, 0, 1, w^2, w, 1, w^2, 1, w^2, 0, 1, w^2, 0, w, 1, w^2, 1, 0, w, 1, 1, w, 0, w^2, 0, 0, 1, 1, w^2, 1, w^2, 1, w^2, w^2, w^2, w, 0, w, 0, w, 0, w^2, 0, w, w, 1, 0, 0, w^2, 1, w^2, w, w^2, w^2, w^2, 1, 1, w^2, w, 1, 1, 0, w, 0, 1, w, 1, w^2, w^2, 0, w, w^2, 0, w, w, 1, w, w, w^2, w, 1, 1, 1, w^2, 1, 0, w, 1, 0, w^2, w, 1, w^2, 0, w^2, w^2, w^2, 0, w, w, w^2, w, w, w^2, w^2, 1, 1, 0, w^2, 0, 0, w^2, 1, 1, w^2, 1, 1, 0, w, 0, w^2, 1, w, w, w^2, 0, w, w^2, w^2, w, w, w, 1, w^2, 1, w^2, w, 1, 1, w, 0, w^2, w^2, 1, w, w, w, w, w^2, 0, w, 0, w^2, 0, 1, 0, 1, 1, 0, 0, 1, 1, w^2, w^2, w, 0, w, w^2, 0, w, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, w, w, w, w^2, w, 0, w^2, 0, w^2, w^2, w^2, w^2, 1, w, 0, 0, w, w^2, 1, w, w, 0, 0, 0, w, 1, w, 0, w, w, 1, w^2, 1, w^2, w, 1, w, w, w^2, 1, 0, w, 1, 1, 0, 0, w, 0, 1, 1, 0, 1, 0, w, 0, 1, 0, w^2, 0, w^2, w^2, 0, w^2, w, 1, w^2, 1, w, 0, w, w^2, w^2, 1, 0, w, 1, w, w, 0, w^2, w^2, 0, 1, w, 1, w, w, w^2, 1, w^2, w^2, w^2, w, w, 1, w, w, w^2, w^2, 0, 1, 0, w^2, w^2, 1, w^2, 0, 1, 0, 1, w^2, w^2, w, w^2, 1, w^2, 1, 0, w, 1, w, 1, w^2, 1, 1, 0, w, w, w, w, 1, 0, 1, 0, 1, w, 0, 0, 0, w^2, 1, 1, 1, 1, w, 1, 1, 1, w, 0, w, w^2, 0, 1, 1, w^2, w^2, 0, w, 0, 0, w, w, w, 0, 0, 1, w^2, w^2, 0, 0, w, w^2, 1, w^2, w^2, w, w^2, 0, 1, 1, 1, w^2, w^2, 0, w, w, 1, w, w, w, 1, 1, w, w^2, w^2, 0, 1, w, w^2, w, w^2, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, w, w^2, w^2, 0, 1, 1, w^2, w^2, 1, 1, 0, 0, 1, w^2, 1, w, 1, 1, 0, w, 0, w^2, w^2, w^2, w, w, 0, w, 0, 1, 1, w^2, w^2, 0, w^2, w^2, w, w^2, 0, w, w, 1, 0, w^2, 1, w, 1, 1, 1, 0, w, w^2, 1, 1, w, 0, w, w^2, w^2, w^2, 0, 0, w^2, w, w, w, w^2, w, w^2, 1, w, w, w^2, w, w, 0, w^2, w^2, 1, 0, 0, w^2, 0, w, w^2, w^2, 1, w^2, w^2, 1, w^2, w^2, 0, w, w, 1, 0, 1, w^2, w, 1, w^2, 0, 0, w^2, 0, 0, w^2, 0, w, w, w, 0, 0, w^2, w, w^2, w^2, w, w, 0, 1, 1, 1, w^2, 0, 0, w, 0, w, 1, w^2, 0, 1, 1, w^2, 0, w^2, w^2, 1, 1, w^2, 1, w, 1, 0, w^2, 0, 1, w, 0, w, 0, 1, 0, w^2, 1, 0, w^2, w^2, 1, 0, 0, w^2, 1, 1, w, 0, 0, w, w, 0, w^2, 1, 0, 0, 1, 0, w, 1, w, w, w^2, w^2, w, 0, 0, w^2, w, w, w, 1, 1, w^2, 0, 0, 0, w, 0, w, w^2, 0, w, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, w, 0, w, w, w^2, w^2, 0, 0, w^2, w^2, w, w, 0, w^2, w, w^2, 1, 1, w, 0, w^2, w^2, 1, w, 1, w^2, 0, 1, w^2, w, w^2, w^2, 1, 0, w, w, 1, w, 1, w^2, 0, w^2, 1, 1, w^2, w^2, 1, 0, w^2, 0, 0, w^2, w^2, w, 1, w^2, w, w^2, 1, 1, w^2, 0, w^2, 0, w^2, 0, w^2, w, 0, 1, 1, 0, w^2, 0, 1, 1, w^2, 0, 1, 1, 0, 1, w, 0, w, w, 0, 1, 1, w, w^2, 1, 1, 0, w, w, w, w^2, w, w^2, w^2, w, w, 1, 0, 0, w, w^2, w, 1, 0, w^2, 0, 1, w, w, w^2, w, 1, w, w, 0, w^2, 1, w, 1, 1, w^2, w^2, w, w, w, 0, w^2, w, w^2, 0, 1, 1, w, w, w^2, w^2, 0, w, 1, w, 1, 0, 0, 0, 0, 1, 1, w^2, 1, w, w^2, 0, 1, 0, 0, w^2, 1, w, 1, w^2, 1, 0, w, 0, 1, 1, 1, w, 1, 0, 0, 0, 1, w, w^2, 1, w^2, 1, w^2, 1, w^2, w^2, 0, w^2, w^2, w^2, w, 0, w^2, w, w, w^2, w, w, 1, w^2, 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, 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, 1, 1, 1, 1, 1, 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, 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, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2012-03-29
Lb(216,9) = 145 is found by truncation of: Lb(219,9) = 148 MST Ub(216,9) = 155 is found by considering shortening to: Ub(215,8) = 155 is found by considering truncation to: Ub(213,8) = 153 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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