lower bound: | 130 |
upper bound: | 137 |
Construction of a linear code [192,9,130] over GF(4): [1]: [192, 9, 130] 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, 0, 1, 0, 1, 0, w^2, 1, w^2, w, w^2, 0, 1, 1, w, w, 1, w, 0, 0, w^2, 1, w, 1, w^2, w, w, w, 1, 1, 1, 1, w, w^2, 0, w, 0, 0, 0, 0, 0, w^2, w, w^2, w, 1, w^2, 0, 1, w, 0, w, 1, 1, 1, 0, w^2, w, 1, w, 1, w^2, w^2, w^2, w^2, w, 0, w, w^2, 0, w, w, 1, 1, 1, 0, w^2, 0, w^2, w, 0, w, w^2, 0, w, w^2, w, w^2, w^2, 1, w^2, w, w, 0, 1, w, w, w^2, w, 1, w^2, 0, w, w^2, 1, w^2, w^2, w, 1, 0, 1, w^2, w^2, 1, 1, w, w, 1, w, w^2, 0, w, w^2, 1, 0, 1, w, w, 0, w, w^2, 0, 0, w^2, 0, 0, w^2, 1, w, 1, w^2, 1, 0, w^2, w^2, 0, w^2, w^2, w, 0, w^2, w, w, w, w^2, w, 1, 0, 1, w, w^2, w^2, w, w, w, w, w, 1, 1, w^2, 1, 0, w^2, w^2, w^2, 1, 1, 1, 0, 0, 1, 1, w^2, 0, 0, w, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, w, 0, 1, 0, 1, w^2, w, 1, 0, w, w^2, w^2, w, w, 0, 1, 0, w^2, 1, 0, 1, 1, 1, w^2, 1, 0, w^2, 0, w, w^2, w, w^2, 1, 0, w^2, 0, w, 1, w, w, 1, w, 0, 1, w, 0, w, w, w^2, 1, 1, 0, w^2, w^2, w^2, 0, w, w^2, 1, 0, 0, w^2, 1, w, w, w^2, w, 0, 0, 1, 0, 0, 0, w^2, w, 1, w^2, 1, 1, 1, 1, 0, 0, w^2, w, 0, 1, w^2, w, w, w, w^2, w, w, 1, 0, 1, w, 1, w, 0, 0, 1, w^2, w, 0, 1, w^2, 0, 0, 1, w, w, 0, w, 0, w^2, 0, w, 1, w^2, 1, w^2, 1, 1, w^2, 0, w, w^2, w^2, 1, w, w, 1, 1, 1, 1, 0, 0, 0, 1, w, 0, 0, 1, w^2, w^2, w, 1, 0, 0, 0, 0, w, w, w^2, 1, 0, w^2, 0, w^2, 1, w^2, 1, 0, 1, 1, 1, w^2, w^2, 1, w^2, w, 1, w, 1, 0, w^2, 0, 1, 0, w^2, w^2, w^2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, w^2, 1, 0, 1, w, w^2, 0, w^2, 1, w, 0, w, 1, 1, w^2, 0, w^2, 1, w^2, 1, w^2, w, w^2, w^2, 1, w, 1, w, 1, 0, 0, w^2, 0, 0, 0, w^2, 1, 0, w^2, 1, 1, w^2, 0, 0, w, 1, w^2, w^2, 0, w^2, w^2, w^2, 1, 1, w, 0, 0, 0, 0, 0, 1, w^2, w^2, w^2, 0, 0, 0, 1, w, w, w, 1, w, 1, w^2, w^2, w, w, 1, 1, w, w^2, 0, w, w, 1, 0, 1, 0, w^2, w^2, 1, 0, w, 0, 1, 1, 0, w, w, 1, w^2, w^2, 0, 0, 1, w, 0, w, 0, 1, 1, w^2, 0, w^2, 0, w, 1, w, w, w, w^2, w^2, w^2, 1, 0, 1, 0, w^2, w^2, w, 0, 1, w, 1, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, w, w^2, w^2, w^2, w^2, 0, 1, w^2, 0, 0, 0, w, 1, w, 1, 1, w^2, w^2, w, w^2, 1, 0, w, w, w^2, 0, 0, 1, 0, w, w, 0, 0, w, 1, 1, 0, w^2, w, 1 ] [ 0, 0, 0, 1, 0, 0, 0, w, 0, 1, 0, 0, 0, 0, w, 0, w^2, 0, 0, w^2, w, 1, 1, w^2, 0, w^2, 0, 0, 0, w, w^2, 1, 0, 1, 1, w^2, w, 1, w, w^2, 1, w, 0, 0, 0, 1, w^2, 0, 1, 0, 0, 0, w^2, w^2, 1, 1, 0, 1, 1, w^2, 0, 0, w, w, 0, w, w^2, 1, w, 1, w, 1, w^2, 0, w, 0, w, 0, 1, w, 1, w^2, 0, w^2, 1, w, w^2, 0, w^2, 1, w, 0, 0, 1, 1, 0, w^2, 1, 0, w, w, w, w, 1, 1, w^2, w, w^2, 1, 1, w^2, 1, w, 1, 0, w^2, 1, 1, 0, w^2, 0, w, 0, 1, w, w, 0, w, w, 1, 0, w, 0, w, w^2, 0, 0, w^2, w, w, w^2, w^2, w, 0, w^2, 1, w^2, w, 0, 1, w, w, 1, 0, w^2, 0, w, 1, 1, w^2, w, 0, 0, w, 1, 1, w^2, w^2, 1, w, w^2, 1, w^2, 1, w, 0, 1, w^2, w, w^2, 1, 0, 0, w^2, 1, 1, 1, w, w, w, w, 0 ] [ 0, 0, 0, 0, 1, 0, 0, w, w^2, 1, 0, w^2, w^2, w, 0, w^2, w, 0, w^2, 0, 1, 1, w, 1, w, w, 0, w, w, 0, 1, w^2, 0, 0, w, 1, w, 0, 1, 0, 0, w, 0, 0, 0, 1, 0, 0, w, 1, w^2, 1, w^2, 1, w^2, 0, 0, 1, 0, w^2, w, w, 0, 1, 0, 1, 0, 1, w^2, w, w, w, w^2, 1, w^2, 0, 0, w, w^2, w, w, w^2, 1, w^2, w, 1, 0, 0, w^2, 0, 1, w^2, w, 1, w, 1, w, 1, 1, 1, w^2, w, 0, w^2, 0, w^2, w^2, w, w^2, w, 1, 1, 1, w^2, 1, w^2, 1, w, w, w, w^2, 0, w^2, 0, w, w, 0, w^2, 1, 1, w, 0, 1, 0, w, 0, w^2, w^2, 1, 1, 0, w, 1, 1, 1, w, w, w^2, 0, w, 1, 1, 1, w^2, 0, w, w^2, 1, 0, 0, w^2, 0, 1, 0, w, 0, 1, 0, w^2, 0, w, w, 1, 1, w^2, 0, 0, w, w, 0, 1, 0, 1, w^2, 0, 0, 0, w^2, 0, 0, 1, w ] [ 0, 0, 0, 0, 0, 1, 0, 0, w, 1, 0, w, w^2, w, 1, 0, 1, w, w, 0, w, 1, w, w, 1, 1, 0, w^2, w^2, w^2, w, 0, w^2, 0, w, 1, w^2, w^2, w^2, w^2, 1, 0, 0, w, 1, 1, w^2, 0, w, 1, w, w, 0, w^2, w, w, w^2, 0, w^2, w^2, w, 1, w^2, w^2, w, w, 0, w, w, w, w^2, 1, w^2, 0, w, w^2, 0, w, 1, 1, w, 0, 1, 0, 1, 0, 1, w, w^2, 0, w, 0, 1, 0, 1, w, 0, 1, 0, 0, 1, w, w^2, w^2, 0, w, w, 1, 0, 0, 0, 0, 0, w^2, w^2, 0, 1, 1, w^2, w, w, 0, w^2, w^2, 0, w^2, 1, 0, w^2, 1, 1, 1, w^2, 1, 1, 1, w, w^2, 1, w, 0, w^2, 1, 0, 0, w^2, w, 0, w^2, 0, w^2, 0, 0, 0, w^2, w, 0, w^2, 1, w^2, 0, 1, 1, w, w^2, w, w, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, w^2, 1, w^2, w, w, 0, w^2, w, w, w^2, 0, w^2, w^2, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 1, w^2, 1, 0, 0, w, w^2, w^2, 0, 1, 0, 1, 1, 0, w^2, 1, w^2, w^2, w^2, 1, w, 0, 1, 1, w^2, w^2, w, 1, 0, w^2, w^2, 1, w, 1, 1, 0, 1, 0, 1, w^2, 1, 0, w^2, w, 0, 1, w^2, 1, w, w, w, 0, 1, 0, w^2, w, 1, w^2, 1, w^2, w, w, w, 0, 1, w^2, 1, w^2, w, w^2, 1, w, w^2, 0, w, 0, 0, w^2, w, 1, 1, w^2, 0, w^2, w^2, w^2, 0, w^2, w^2, 0, w^2, w^2, w^2, 1, 1, 0, 1, 1, w, 1, w, w^2, w^2, w, w^2, 0, w^2, w^2, w^2, 0, 1, w^2, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, w, w, 1, 1, w^2, w^2, 0, 1, 1, 0, w^2, 1, w^2, w, 1, w^2, 0, 1, 0, 0, w^2, 0, 1, w^2, 0, 0, 1, 1, w^2, 1, w^2, w^2, w, w^2, 0, 0, 0, w^2, 1, 0, w, 0, 1, w, w^2, 0, 1, 1, w^2, w^2, 1, w^2, w^2, 0, w, 0, w^2, 0, w, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, 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, w^2, w, 1, w^2, w^2, w^2, 0, 0, w, 0, 1, w, 1, 0, w, 1, 1, w^2, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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, 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, 0, 1, 1, 0, 1, 0, 0, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2008-06-13
Lb(192,9) = 129 is found by truncation of: Lb(193,9) = 130 MST Ub(192,9) = 137 is found by considering shortening to: Ub(191,8) = 137 is found by considering truncation to: Ub(190,8) = 136 Da1
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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