lower bound: | 68 |
upper bound: | 73 |
Construction of a linear code [104,8,68] over GF(4): [1]: [108, 8, 72] Linear Code over GF(2^2) Code found by Plamen Hristov Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, w, w^2, 1, 0, 1, 1, w, w, 0, w, w^2, w, 1, w^2, w, 1, 0, 0, 0, w, 0, w^2, 1, 0, 0, 1, w, w, w^2, 0, w^2, w, 1, 1, 1, w, w, 1, 1, 0, w^2, 0, w, 1, w, w^2, w^2, w^2, 0, w^2, w^2, 1, 1, 1, w^2, w, 1, 1, 0, 0, 0, w^2, 0, w^2, 0, 0, w, 1, 1, w, w^2, 0, 1, w, w^2, 0, w, 0, 1, 0, 0, 0, w, w, 1, 0, w^2, 1, 0, w, 0, w, 1, 0, w, 1, 1, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, w^2, w, 0, 0, 0, 1, w^2, w, 0, w^2, w, 1, 0, w^2, 1, w^2, w, 1, 1, 0, 0, 1, w, w, 0, 1, 0, w^2, 0, w^2, 0, w^2, w, w, w, w, w, 0, w^2, 1, w, 1, w, w^2, 1, 1, 0, 0, 1, 1, w^2, w, 1, 0, w, 1, w^2, w, 1, w, 1, 0, 0, w, w^2, w, w^2, 0, 1, 1, w, 0, 0, w^2, w^2, 0, 0, w^2, 1, w, w^2, 1, 0, 0, 1, w^2, 1, 1, w, 0, 1, 1, w, 1, 1, 1, 1, w, w^2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, w^2, w, 0, 0, 0, 1, w^2, w, 0, w^2, w, 1, w, w^2, 1, w^2, w, 1, 1, 0, 0, 1, w, w, 0, 1, 0, w^2, 0, w^2, 0, w^2, w, w, w, w, w, 0, w^2, 1, w, 1, w, w^2, 1, 1, 0, 0, 1, 1, w^2, w, 1, 0, 0, 1, w^2, w, 1, w, 1, 0, 0, w, w^2, w, w^2, 0, 1, 1, w, 0, 0, w^2, w^2, 1, 0, w^2, 1, w, w^2, 1, 0, 0, 1, w^2, 1, 1, w, 0, 1, 1, w, 1, 1, 1, w^2, 1, w ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, w^2, 0, w^2, w, w, 1, 1, w, 0, w, w^2, w, 0, 0, w, 1, w^2, w^2, w^2, 1, 1, w^2, w^2, 0, 0, 1, w, 1, 1, 1, 0, w, w^2, w, w^2, w^2, 1, w, 0, w^2, 0, w, w^2, w^2, w, w^2, 1, w, 1, w^2, 0, 1, w^2, w, 1, 1, 0, w^2, 1, 0, 1, 1, w, 1, w, w^2, 0, w, w^2, 1, w, w, 0, w^2, w, 0, w, w, 1, w^2, w^2, 1, w^2, 0, w^2, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, w^2, w, 0, 1, 1, 0, w, w^2, 0, w, w, w^2, 1, 0, w, w, w, w, 1, w^2, w, w^2, w^2, w^2, w, 1, w, 0, w, w^2, 0, 1, 1, 0, w, 1, w, 1, 0, w, w, 1, w^2, 1, 0, 0, 1, 0, w^2, w, 1, 1, w, 0, 1, 1, w, w^2, w^2, 1, w, w, w^2, w^2, 1, w^2, 0, 0, 0, w, 0, 1, 1, w^2, 0, w, w^2, w, w, 0, w, w^2, w^2, 0, w^2, 0, 0, w^2, 0, 0, w, w^2, w, w^2, w^2, w, w, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, w, w^2, w^2, w, 0, 0, w^2, w^2, w^2, 1, w^2, w^2, w^2, w, 1, 0, w^2, 0, w, w, w, w, w^2, w^2, 1, w^2, w^2, 0, w, 1, 1, w, w, w^2, 0, w^2, w, 1, w, 0, w^2, 0, w^2, w, w, 1, w, 1, 1, 0, 0, w, w^2, w^2, w^2, 1, 1, w, w^2, 0, w^2, w^2, 1, w^2, w, w, w^2, 1, 0, w, w, w^2, w^2, 0, w^2, w, w, 0, 1, w^2, 0, w, 0, w, 0, 0, w, w^2, 1, w, w^2, w^2, 0, 1, 1, w, 0, 0, w, w ] [ 0, 0, 0, 0, 0, 0, 1, 0, w^2, 1, w, 1, 1, 0, w^2, 0, w, w, 1, w, 1, w, 1, w^2, 1, 0, 0, w, w, w^2, w, 1, 0, 1, w^2, 0, 1, w^2, w^2, 1, 0, w^2, 0, w^2, 0, w^2, 0, 1, w^2, w^2, w, w^2, w^2, 1, 0, 0, w^2, w^2, 0, w, 0, 0, 0, 1, w^2, 0, 1, 0, 0, w^2, w^2, w^2, w^2, 0, w, w^2, 0, w^2, 1, w^2, 1, w^2, w^2, w, w, w, 1, 1, 0, 0, w, 0, w^2, 1, w^2, w, 1, w, w, w, w^2, 1, w, 1, w^2, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 1, w, w^2, 1, 0, 1, 1, w, w, 0, w, w^2, 1, 1, w^2, w, 1, 0, 0, 0, w, 0, w^2, 1, 0, 0, 1, w, w, w^2, 0, w^2, w, w, 1, 1, w, w, 1, 1, 0, w^2, 0, w, 1, w, w^2, w^2, w^2, 0, w^2, w^2, 1, 1, 1, w^2, w, 1, 1, 0, 0, 0, w^2, 0, w^2, 0, 0, w, 1, 1, w, w^2, 0, 1, w, 1, 0, w, 0, 1, 0, 0, 0, w, w, 1, 0, w^2, 1, 0, w, 0, w, 1, 0, w, w^2, 0, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [104, 8, 68] Linear Code over GF(2^2) Puncturing of [1] at { 105 .. 108 } last modified: 2008-04-25
Lb(104,8) = 67 is found by truncation of: Lb(106,8) = 69 MST Ub(104,8) = 73 follows by a one-step Griesmer bound from: Ub(30,7) = 18 is found by considering shortening to: Ub(28,5) = 18 is found by considering truncation to: Ub(26,5) = 16 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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