lower bound: | 57 |
upper bound: | 61 |
Construction of a linear code [88,8,57] over GF(4): [1]: [88, 8, 57] 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, 1, 0, w^2, w^2, w^2, w, 1, 1, 0, w, w^2, w, 0, 1, 0, w, 1, 1, w^2, w, w^2, w, 0, 0, 1, 1, w, 1, 0, w^2, 1, w, 1, w, 0, w, 1, 1, w, w^2, 1, 1, w^2, 0, w^2, 1, w^2, 1, w, 0, 1, w^2, 1, 1, 0, 0, w^2, w, w^2, w, 1, 1, w^2, 0, 1, 0, w^2, w, w^2, 0, 1, 1, w^2, w, w, w, 0, 0, w, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, w^2, w^2, w^2, w, 1, 1, 0, w, w^2, w, 0, 1, 0, w, 1, 1, w^2, w, w^2, w, 0, 0, 1, 1, w, 1, 0, w^2, 1, w, 1, w, 0, w, 1, 1, w, w^2, 1, 1, w^2, 0, w^2, 1, w^2, 1, w, 0, 1, w^2, 1, 1, 0, 0, w^2, w, w^2, w, 1, 1, w^2, 0, 1, 0, w^2, w, w^2, 0, 1, 1, w^2, w, w, w, 0, 0, w ] [ 0, 0, 1, 0, 0, 0, 0, 0, w, 0, 0, 1, w, 0, 1, 0, 1, w, 1, 1, w^2, 0, 0, w, w, 0, 0, w, w, 1, w^2, w, w, w, w, w^2, w, 0, w, 0, w^2, 1, 1, 1, w, 0, w, 0, 0, 1, 0, 1, w, w, w, w^2, 0, 1, 0, 1, w^2, 1, 1, 1, 1, w^2, w, 1, 1, 0, 0, 1, 1, 0, 0, w^2, w, w, 1, w, 0, w, 0, 1, w, 0, w^2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, w, w, 1, 1, 0, 1, w, w^2, 0, w, w^2, w, 1, 1, 0, w^2, 0, 0, 1, w^2, w^2, 1, 1, w^2, 0, 0, 1, 0, w^2, w^2, w, 1, w, 0, 1, w, w^2, 0, w^2, w^2, w, w, 0, 0, 0, 0, w^2, 0, 0, 0, w^2, 1, w^2, 1, 1, 1, 0, w, w, 1, w^2, w^2, 1, 0, w^2, 1, 1, w^2, w, w, 0, w^2, w^2, w^2, 1, w^2, 1, 1, w^2, w ] [ 0, 0, 0, 0, 1, 0, 0, 0, 1, w, 1, w, w, w, 0, w^2, w^2, w, 1, 1, w, 0, 1, w, w, 1, w^2, w^2, 0, 1, 1, 1, w, 1, w, 0, 0, 0, w, 0, 0, 0, 0, w^2, w^2, w, w, 0, w, w^2, 1, 0, w^2, 1, w^2, w, w, 0, 1, 0, 0, w, 1, 1, w, w, 1, 0, 0, w, 0, 1, 1, w^2, w, w^2, 0, w, w^2, 1, 0, 1, 1, w^2, w^2, 0, w^2, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, w^2, 1, 0, w^2, 0, w^2, 1, w^2, w^2, w, 0, 0, 1, 1, 0, 0, 1, 1, w^2, w, 1, 1, 1, 1, w, 1, 0, 1, 0, w, w^2, w^2, w^2, 1, 0, 1, 0, 0, w^2, 0, w^2, 1, 1, 1, w, 0, w^2, 0, w^2, w, w^2, w^2, w^2, w^2, w, 1, w^2, w^2, 0, 0, w^2, w^2, 0, 0, w, 1, 1, w^2, 1, 0, 1, 0, w^2, 1, 0, 0, w^2, w, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, w^2, w^2, w^2, w, 1, 1, 0, w, w^2, w, 0, 1, 0, w, 1, 1, w^2, w, w^2, w, 0, 0, 1, 1, w, 1, 0, w^2, 1, w, 1, w, 0, w, 1, 1, w, w^2, 1, 1, w^2, 0, w^2, 1, w^2, 1, w, 0, 1, w^2, 1, 1, 0, 0, w^2, w, w^2, w, 1, 1, w^2, 0, 1, 0, w^2, w, w^2, 0, 1, 1, w^2, w, w, w, 0, 1, 0, w^2, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, w^2, w^2, w^2, w, 1, 1, 0, w, w^2, w, 0, 1, 0, w, 1, 1, w^2, w, w^2, w, 0, 0, 1, 1, w, 1, 0, w^2, 1, w, 1, w, 0, w, 1, 1, w, w^2, 1, 1, w^2, 0, w^2, 1, w^2, 1, w, 0, 1, w^2, 1, 1, 0, 0, w^2, w, w^2, w, 1, 1, w^2, 0, 1, 0, w^2, w, w^2, 0, 1, 1, w^2, w, w, w, 0, 1, w, w^2, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2006-10-04
Lb(88,8) = 57 MST Ub(88,8) = 61 follows by a one-step Griesmer bound from: Ub(26,7) = 15 is found by considering shortening to: Ub(25,6) = 15 is found by considering truncation to: Ub(23,6) = 13 BGV
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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