lower bound: | 124 |
upper bound: | 131 |
Construction of a linear code [184,9,124] over GF(4): [1]: [185, 9, 125] Linear Code over GF(2^2) code found by Tatsuya Maruta Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, w^2, 0, w^2, w^2, w, w, 0, 1, w^2, 1, 1, 0, 0, w^2, 1, 0, 1, w^2, 0, 1, w, w, w^2, 1, w, 1, w^2, 0, 1, w, 1, 1, 0, w, 0, 0, 0, 1, 1, 0, w, 1, w^2, 0, w, w^2, 0, 0, w^2, 0, w, w^2, w^2, w^2, w, w, 1, w, w, w, w^2, 0, w^2, w^2, 0, 0, w, w, 1, 1, w^2, w, w, w, 0, w, w^2, w^2, w, 0, w, 1, 1, w, 0, w, w, w, 1, w^2, w^2, w, w, 0, 0, 1, 1, 0, 1, w, w, w, w^2, w, w, 1, 1, 1, w, 0, 1, 0, 0, 1, w, 0, 1, w^2, w, 0, w^2, w^2, 0, 0, 0, w, 0, w^2, w^2, w, w^2, 0, 1, w^2, w, w^2, 1, w, w, w^2, 0, 1, w^2, 0, w^2, 1, 0, 0, w^2, w^2, 1, w^2, 0, w, w, 1, 1, 0, 1, 0, w^2, 1, 1, w, 1, w^2, 0, 0, 0, 1, 1, 1, w, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, w, 0, w^2, 0, w^2, w^2, w, w, 0, 1, w^2, 1, 1, 0, 0, w^2, 1, 0, 1, w^2, 0, 1, w, w, w^2, 1, w, 1, w^2, 0, 1, w, 1, 1, 0, w, 0, 0, 0, 1, 1, 0, w, 1, w^2, 0, w, w^2, 0, 0, w^2, 0, w, w^2, w^2, w^2, w, w, 1, w, w, w, w^2, 0, w^2, w^2, 0, 0, w, w, 1, 1, w^2, w, w, w, 0, w, w^2, w^2, w, 0, w, 1, 1, w, 0, w, w, w, 1, w^2, w^2, w, w, 0, 0, 1, 1, 0, 1, w, w, w, w^2, w, w, 1, 1, 1, w, 0, 1, 0, 0, 1, w, 0, 1, w^2, w, 0, w^2, w^2, 0, 0, 0, w, 0, w^2, w^2, w, w^2, 0, 1, w^2, w, w^2, 1, w, w, w^2, 0, 1, w^2, 0, w^2, 1, 0, 0, w^2, w^2, 1, w^2, 0, w, w, 1, 1, 0, 1, w, w^2, 1, 1, w, 1, w^2, 0, 0, 0, 1, 1, 1, w ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w, w, w, w, 1, w, w, 0, 1, 1, w, w^2, w^2, w, w, 1, 0, 1, 0, 0, 1, w, w, 0, 1, 0, 1, w, 1, 1, 0, 0, w, 0, w^2, w^2, 1, 0, w^2, 0, 1, w, w, w, w^2, w, 0, w, w, 0, 1, w, w, 1, w^2, 0, w^2, 0, w, 1, w, w^2, w^2, 1, 1, 1, 1, w^2, 0, w, w^2, w, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 1, w^2, 1, 0, w^2, w, w, w, w, w^2, w^2, 1, w, 1, 0, w^2, 0, w^2, w, 1, 1, w, 0, 1, 1, 0, 1, w^2, 1, 1, 1, w, 0, w^2, 0, w, w^2, w^2, 0, 1, 0, 0, w, w, 1, w, 0, w, 0, 1, 1, w, 0, 0, w, 0, w, 1, 1, w^2, w^2, 1, w, w, 0, 1, 1, w, 1, 1, 1, 1, w, 0, w^2, 1, 0, 0, w, 0, 1, w^2, 0, w^2, w^2, w, 0, w ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w, w, w, w, 1, w, w, 0, 1, 1, w, w^2, w^2, w, w, 1, 0, 1, 0, 0, 1, w, w, 0, 1, 0, 1, w, 1, 1, 0, 0, w, 0, w^2, w^2, 1, 0, w^2, 0, 1, w, w, w, w^2, w, 0, w, w, 0, 1, w, w, 1, w^2, 0, w^2, 0, w, 1, w, w^2, w^2, 1, 1, 1, 1, w^2, 0, w, w^2, w, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 1, w^2, 1, 0, w^2, w, w, w, w, w^2, w^2, 1, w, 1, 0, w^2, 0, w^2, w, 1, 1, w, 0, 1, 1, 0, 1, w^2, 1, 1, 1, w, 0, w^2, 0, w, w^2, w^2, 0, 1, 0, 0, w, w, 1, w, 0, w, 0, 1, 1, w, 0, 0, w, 0, w, 1, 1, w^2, w^2, 1, w, w, 0, 1, 1, w, 1, 1, 1, 1, w, w^2, w^2, 1, 0, 0, w, 0, 1, w^2, 0, w^2, w^2, w, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, w, 0, w, 0, w^2, w^2, w^2, 0, w, w^2, 1, 0, w^2, w, 0, w, 0, w, w, 0, w, w^2, w^2, w, w, 1, w, 0, 1, w, 1, w^2, 1, 0, w, w^2, 1, 0, 0, w^2, 1, w^2, 1, 0, w^2, w^2, w, w, w, w, 1, w^2, 0, w^2, 1, 1, w, w^2, w^2, 0, w^2, 1, w^2, w^2, w^2, 1, 1, w, 1, 1, 0, 0, w, w^2, 1, w, w, 1, 1, 0, 0, 0, 0, w, w, 1, 1, w, w^2, 1, 0, 0, w, w, 1, w, w, w^2, w^2, w^2, w, w^2, 0, w^2, w^2, 1, w, w, w^2, 0, w^2, w, 1, 1, 1, 1, w^2, w^2, 0, w, w^2, w, w^2, 0, 0, w, w^2, 1, 0, w, w^2, w, 1, w, 0, 1, w, 1, 1, w^2, w^2, 1, 0, 1, 1, 0, 1, 0, 1, w^2, 0, w, w^2, 1, 0, w^2, w^2, w^2, 0, 1, 0, 1, w^2, w, w, w^2, 1, w^2, w, 0, 1, w, 1, w, 1, w^2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w, w, w, w, 1, w, w, 0, 1, 1, w, w^2, w^2, w, w, 1, 0, 1, 0, 0, 1, w, w, 0, 1, 0, 1, w, 1, 1, 0, 0, w, 0, w^2, w^2, 1, 0, w^2, 0, 1, w, w, w, w^2, w, 0, w, w, 0, 1, w, w, 1, w^2, 0, w^2, 0, w, 1, w, w^2, w^2, 1, 1, 1, 1, w^2, 0, w, w^2, w, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 1, w^2, 1, 0, w^2, w, w, w, w, w^2, w^2, 1, w, 1, 0, w^2, 0, w^2, w, 1, 1, w, 0, 1, 1, 0, 1, w^2, 1, 1, 1, w, 0, w^2, 0, w, w^2, w^2, 0, 1, 0, 0, w, w, 1, w, 0, w, 0, 1, 1, w, 0, 0, w, 0, w, 1, 1, w^2, w^2, 1, w, w, 0, 1, 1, w, 1, 1, 1, 1, w, 0, 0, 0, w, 0, w, 0, 1, w^2, 0, w^2, w^2, w, 0, w, 1, w, w^2, w ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, w, w, w, w, 1, w, w, 0, 1, 1, w, w^2, w^2, w, w, 1, 0, 1, 0, 0, 1, w, w, 0, 1, 0, 1, w, 1, 1, 0, 0, w, 0, w^2, w^2, 1, 0, w^2, 0, 1, w, w, w, w^2, w, 0, w, w, 0, 1, w, w, 1, w^2, 0, w^2, 0, w, 1, w, w^2, w^2, 1, 1, 1, 1, w^2, 0, w, w^2, w, w^2, w, 0, w, w^2, w^2, w^2, 1, 0, 1, w^2, 1, w^2, 1, 0, w^2, w, w, w, w, w^2, w^2, 1, w, 1, 0, w^2, 0, w^2, w, 1, 1, w, 0, 1, 1, 0, 1, w^2, 1, 1, 1, w, 0, w^2, 0, w, w^2, w^2, 0, 1, 0, 0, w, w, 1, w, 0, w, 0, 1, 1, w, 0, 0, w, 0, w, 1, 1, w^2, w^2, 1, w, w, 0, 1, 1, w, 1, 1, 1, 1, w, 0, 0, 0, w, 0, w, 0, 1, w^2, 0, w^2, w^2, w, 0, w, 1, w, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, w, 0, w, w, 1, 1, 0, w^2, w, w^2, w^2, 0, 0, w, w^2, 0, w^2, w, 0, w^2, 1, 1, w, w^2, 1, w^2, w, 0, w^2, 1, w^2, w^2, 0, 1, 0, 0, 0, w^2, w^2, 0, 1, w^2, w, 0, 1, w, 0, 0, w, 0, 1, w, w, w, 1, 1, w^2, 1, 1, 1, w, 0, w, w, 0, 0, 1, 1, w^2, w^2, w, 1, 1, 1, 0, 1, w, w, 1, 0, 1, w^2, w^2, 1, 0, 1, 1, 1, w^2, w, w, 1, 1, 0, 0, w^2, w^2, 0, w^2, 1, 1, 1, w, 1, 1, w^2, w^2, w^2, 1, 0, w^2, 0, 0, w^2, 1, 0, w^2, w, 1, 0, w, w, 0, 0, 0, 1, 0, w, w, 1, w, 0, w^2, w, 1, w, w^2, 1, 1, w, 0, w^2, w, 0, w, w^2, 0, 0, w, w, w^2, w, 0, 1, 1, w^2, w^2, 0, w^2, 0, 1, 0, w^2, 1, w^2, w, 0, 0, 0, w^2, w^2, w^2, 1, w^2, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, w, 0, w, w, 1, 1, 0, w^2, w, w^2, w^2, 0, 0, w, w^2, 0, w^2, w, 0, w^2, 1, 1, w, w^2, 1, w^2, w, 0, w^2, 1, w^2, w^2, 0, 1, 0, 0, 0, w^2, w^2, 0, 1, w^2, w, 0, 1, w, 0, 0, w, 0, 1, w, w, w, 1, 1, w^2, 1, 1, 1, w, 0, w, w, 0, 0, 1, 1, w^2, w^2, w, 1, 1, 1, 0, 1, w, w, 1, 0, 1, w^2, w^2, 1, 0, 1, 1, 1, w^2, w, w, 1, 1, 0, 0, w^2, w^2, 0, w^2, 1, 1, 1, w, 1, 1, w^2, w^2, w^2, 1, 0, w^2, 0, 0, w^2, 1, 0, w^2, w, 1, 0, w, w, 0, 0, 0, 1, 0, w, w, 1, w, 0, w^2, w, 1, w, w^2, 1, 1, w, 0, w^2, w, 0, w, w^2, 0, 0, w, w, w^2, w, 0, 1, 1, w^2, w^2, 0, w^2, 0, 1, w^2, w^2, 1, w^2, w, 0, 0, 0, w^2, w^2, w^2, 1, w^2, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [184, 9, 124] Linear Code over GF(2^2) Puncturing of [1] at { 185 } last modified: 2006-10-04
Lb(184,9) = 124 is found by truncation of: Lb(185,9) = 125 MST Ub(184,9) = 131 is found by considering shortening to: Ub(183,8) = 131 is found by considering truncation to: Ub(182,8) = 130 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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