lower bound: | 139 |
upper bound: | 144 |
Construction of a linear code [200,8,139] over GF(4): [1]: [201, 8, 140] 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, 0, w, 1, w, 1, w, w^2, w, w, 0, w^2, w^2, w^2, 1, 1, w^2, w^2, 1, 1, w, 1, w, w^2, 1, w^2, 1, 0, 0, w, w, 1, w^2, w, w^2, 1, w, 1, 1, 0, w^2, 1, 1, w^2, 0, 0, w^2, w^2, 1, w, 0, w, 0, w, 1, 0, w, w, 1, w^2, w, 0, 1, 0, 0, 0, w^2, w^2, 0, 0, 1, 0, 1, w, 0, w, 1, 1, w, w^2, 1, 0, 0, w^2, w, 0, 0, w, w, w^2, 0, w, 1, w^2, w, w, w^2, 0, w, w^2, 1, w^2, w, 1, 1, 1, 1, w, 1, 0, 0, w, w^2, 1, w^2, w^2, 0, 0, w, w^2, 0, 0, 0, w^2, w^2, w, 1, w, 0, 0, 0, w, 1, 0, 0, w, w, w, w, w, w^2, w^2, w, w, w, w, 0, w^2, 1, w, 0, 1, w^2, 1, w^2, 0, 1, 1, 1, w, w, w^2, 1, w, 0, w, 0, w^2, w, w, 0, w^2, 1, w^2, w, 0, w^2, 0, 1, w^2, w^2, 0, 1, w, w^2, 0, 0, w, w, w^2, w^2, 1, w, w^2, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, w^2, 1, 1, w^2, w, 0, w, 1, 1, w, 0, w^2, w^2, w, w^2, w^2, 0, w^2, 1, 0, w^2, 0, 1, 0, 0, 1, 1, w, 0, 0, w, w, w, 1, 1, w, w^2, 1, 1, 0, w^2, 0, w^2, 0, w, 0, 0, w^2, w^2, 0, w^2, w^2, 0, w^2, 1, 1, w, w^2, w, w^2, 1, 0, w, 0, w, 0, w, 0, w, w^2, 1, 0, 1, w^2, w^2, w^2, w^2, 1, w, w^2, 0, w, w, 1, 0, 1, w, 0, 1, 1, 0, 0, w^2, 0, 0, 1, 0, 0, w^2, w, 1, 1, 1, 1, w^2, w, w^2, w^2, w, 0, w, w^2, 0, w, w, w^2, 0, w^2, w^2, 0, 0, 1, w^2, w^2, 1, w^2, w^2, 1, 0, w^2, 0, 1, w, w, 0, 1, w^2, 1, 1, w^2, w^2, w^2, w^2, w^2, 1, 1, 1, 1, w^2, w^2, 0, 1, 0, 0, w, w, w^2, w^2, 1, 0, w^2, 0, 1, w^2, 1, w, w, 0, 0, w, 0, 1, w, w^2, w, w^2, 0, 1, 0, w, 1, 1, 1, 0, w, 1, w, 0, 0, 0, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, w^2, 1, w, w, 0, 1, w^2, 1, 0, 0, w^2, 1, w, w^2, w, w^2, w, 1, w^2, 1, 0, w^2, 0, w^2, w, w, w^2, w, 1, 1, 1, w^2, w^2, w^2, 1, 1, w, w, 0, 1, 0, w^2, 0, w^2, w, 0, w, w, 0, 0, 1, w, w, 1, w, 0, 0, w^2, w^2, w, w^2, 1, 0, w, w, 0, w, 1, w^2, 1, w, 0, 1, 0, w, w, w^2, w^2, 1, w^2, w, 0, w, w, w^2, w, w^2, 0, w^2, w, w, w^2, w^2, 0, 1, 1, 0, 0, 0, w^2, w^2, 0, 0, 0, 1, 1, 0, 1, 1, 0, w, 1, 0, 1, w^2, w^2, w, 1, w, w, 1, 0, 1, w^2, w^2, w^2, 1, 1, w^2, w, 0, w^2, w, 1, 1, 1, 0, w, 0, 0, w, w^2, w^2, w^2, w^2, 1, w^2, w^2, w^2, 1, 0, w^2, w, w^2, w^2, 1, w^2, w, w, 0, 1, w^2, 0, 1, w^2, 1, w, 0, w, w, 1, w^2, w, 1, 0, w^2, w, 1, 0, 1, w^2, 1, 1, 1, 0, 0, w^2, w^2, 1, w, w^2, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, w, 1, 1, 1, 1, w^2, w, 0, 0, w, w, w, w^2, w, w^2, w^2, 1, 0, w^2, w, 0, 0, 0, 1, w^2, 1, w, 0, w^2, w, w^2, 1, w, w, 0, w^2, 1, 1, w^2, 0, 0, w, 1, w^2, 1, 1, w, 1, w^2, 1, 0, 1, w, 0, w^2, w, w, w, 0, 1, w^2, w^2, 1, w, w, 1, w^2, 0, w^2, 1, 0, w, 0, 0, 1, w, w^2, w, 0, w^2, w, 0, 1, w, 1, 0, 1, 1, 1, w^2, 1, w^2, 1, 1, w, w^2, w, 0, w, 0, 1, 0, w, 1, 1, w^2, w, 1, 0, w^2, 0, w^2, 0, w, 1, w, 0, w, w^2, 0, 0, 1, w^2, 1, w^2, w, 0, w^2, w, 1, 0, 1, w, 0, 1, 0, 0, 1, w, 1, w, w^2, 0, 1, 0, 0, 0, w^2, w^2, w, w^2, 0, 1, w, w, 1, w^2, 1, 0, w^2, w, 1, 0, w^2, w, w, w, w^2, 0, w, 1, w, 1, w^2, w, w, w^2, 0, 1, 1, w, 1, 0, w^2, w, 0, w^2, 1, 1, 0, w, w ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, w^2, w, w^2, 0, w, w^2, 1, 1, 0, 1, w^2, 1, 0, 0, 0, 0, w, w, 1, 0, w, 1, 1, w^2, w, 1, w, 1, w^2, w, w, w, 0, 0, 0, w, w, 0, w, 0, 1, 1, w, 1, w, 1, w^2, 1, w^2, 0, 1, w, 0, w^2, w, 1, 0, w, w, w^2, 0, w^2, 0, 1, 1, w^2, w^2, w, 1, 1, 1, 0, w, 1, 0, 1, 1, w^2, w^2, w, w, 1, 0, w^2, 1, 1, w^2, 0, w, 1, 0, 0, w^2, 1, w, w, w, 0, w^2, 0, 1, 0, w^2, 0, w^2, 1, w, w, 1, 0, w^2, 1, 0, 0, 0, w, w^2, w, 1, 1, 0, 1, w^2, w^2, w^2, w^2, 0, w^2, 1, 0, w, w, 0, 1, w, 1, w, w, 0, 1, w^2, 0, 0, w^2, 0, w, w^2, 0, w, w^2, 1, w^2, 1, 1, 0, w^2, w, w^2, 0, 1, w, 1, w^2, w, 1, 0, 1, 0, 1, 1, w, 1, w, 0, 0, 0, w^2, w, 0, 1, w, 1, w, w^2, w, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w, 0, 1, 0, w, 0, w, w, 0, 0, 1, 1, 0, w^2, w^2, w, w^2, 1, 1, 1, 0, 1, w, w, 1, 1, 0, 0, 1, 1, w^2, 0, w^2, 1, w, 0, 1, w, 1, w, w^2, w, w^2, 0, 1, 0, w, 1, w, 0, 1, 0, w, w, 1, w, w^2, w, 0, 1, 0, w, w, 1, w^2, w^2, w, 0, 0, w, 1, w, w, 0, w, w, 1, w^2, 0, w, 0, w^2, 1, 0, 1, 0, 1, w^2, 1, 0, w^2, w^2, w^2, w^2, w, w^2, 1, 0, w^2, 1, 1, w^2, w^2, 1, 1, 1, w^2, 1, w^2, 1, 0, 1, 0, w, w^2, w, w, w, w^2, 1, 1, w, w^2, 1, 0, 1, w^2, w, 0, 1, w^2, w, 0, w, w, 1, 1, 0, 1, w, 1, w, w, 1, 1, w, w^2, 0, w, 0, 1, 1, w^2, 0, 0, w^2, w, w, w, w, w, w^2, 1, w^2, 0, 1, w^2, 0, 0, w, 0, w^2, 1, 1, w^2, w^2, w^2, 0, 1, w, 0, 1, 0, w^2, 0, w, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 1, w^2, 0, 1, 0, 0, 0, w, 0, 1, w, w^2, 0, 1, w, w, 0, 1, 1, 0, 0, 1, 1, 0, w^2, 0, 1, w, w^2, w^2, w^2, w, 1, 1, w^2, 1, 0, w, w^2, w^2, 0, w^2, w, w, w^2, 0, w, w, w, w, 0, w^2, 1, 1, 0, 0, 0, 1, w, w, w, 1, w, w, 1, w, 1, w^2, w, w^2, 0, 0, 1, 0, 1, w^2, 0, w, 1, w, w, 0, w, w^2, 0, w^2, w^2, w^2, 1, w^2, w, w, w, 0, 1, 0, w^2, w, w, 0, w^2, w^2, 1, 1, 0, 1, w^2, w, w, 1, w, w, 1, 1, w^2, 0, w, w, 1, 1, w, 0, 1, 1, 0, w^2, w, 1, w, w^2, 1, 1, w, w^2, 1, 0, w, 1, w, w, w^2, w, 1, w^2, 1, 0, 0, 1, w^2, 0, 0, w, w^2, w^2, 1, w, 0, w^2, w, w^2, 0, 0, 1, w, 1, w^2, w, 0, 0, 1, w^2, 1, w^2, 1, w, w, w^2, w^2, w^2, 1, 0, 0, w^2, 1, 0, 0, w^2, w, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, w, 1, 0, w^2, w, w, w^2, 0, w, 1, w^2, w^2, 1, 1, 1, w, w^2, w^2, w, w^2, w, 1, 1, w, 1, 1, 1, w^2, 0, w^2, w^2, 1, 0, w, w^2, w^2, w^2, w^2, w, w, w, w, w, 1, w, w^2, 1, w^2, w^2, 1, 1, 1, w^2, 0, 1, 1, 1, w^2, w^2, w, w, w, w^2, 0, 1, w, 0, 0, w^2, 0, 1, w, w^2, w, 0, 1, w^2, 1, 0, 0, 0, w^2, 0, 1, w, w^2, w^2, 1, 0, 1, w^2, 1, w^2, 0, w^2, 0, w, 0, w, 1, 0, w^2, w^2, 1, 0, w^2, 1, w, w, 0, 1, 0, 0, 1, w^2, 1, 1, 0, w^2, w^2, w, 0, w, 0, 0, w, 0, 1, w, 1, w, w^2, 0, 0, w^2, 1, w, w, w, 1, 0, 0, w, w^2, 0, w, 1, w, w^2, w^2, w^2, 0, w, 0, w^2, w^2, 1, 0, w, w^2, 0, 0, w^2, 1, 0, 1, w^2, 1, 0, w, 0, w^2, 0, w, w, 0, 1, 1, 1, w^2, 0, 1, w^2, w, w^2, 0, w, w, 0, w^2, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [200, 8, 139] Linear Code over GF(2^2) Puncturing of [1] at { 201 } last modified: 2013-03-13
Lb(200,8) = 135 is found by taking a subcode of: Lb(200,9) = 135 MST Ub(200,8) = 144 is found by considering truncation to: Ub(198,8) = 142 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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