lower bound: | 104 |
upper bound: | 108 |
Construction of a linear code [128,6,104] over GF(8): [1]: [128, 6, 104] Linear Code over GF(2^3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w^3, w^6, 1, w^2, 0, w^6, 0, w, w^5, 1, w^2, w^4, 1, w, w^4, w^6, 0, w^6, w^3, w^6, w, w^6, w^6, w^2, w^6, w^2, w^3, w^6, w^4, w^2, w^4, w^2, w^5, 0, w^5, w^4, w, w^5, w^6, w^5, w^4, 1, w^3, w^2, 1, w^4, w, 1, w, w^5, w^5, 1, w^4, w^3, w^4, 1, w^3, w, w^6, w^2, w^3, w^4, w^3, 0, 1, 1, w^4, w^4, w^6, 0, w, w^5, w, 0, w^4, w^6, w^5, w^5, 0, 0, 1, w^5, 0, w^2, w^4, w^6, w^5, w^6, w^2, w, w^6, w, w^3, 1, w^2, w^3, w^5, w^5, w^3, w, w^3, 0, 0, w^2, w^2, 1, w^6, w^4, w^4, 0, w^5, w^2, w^4, 0, w^3, 1, w, w^5, 0, w^6, w^5, w^5 ] [ 0, 1, 0, 0, 0, 0, w^4, w^4, w^3, w, w, w^5, w^3, 1, w^5, w^2, w^5, 1, 0, w^5, w^2, 0, 0, w^6, 0, 0, w^3, w^3, w, 0, 1, w^6, w^3, 0, w, w^5, w, w^6, w, w^6, w^3, w^2, w^2, w^3, w^5, w^2, w^2, w^3, 1, 0, w^3, 0, w^3, w^6, 0, w^4, w^2, w^5, w^2, 1, 0, 1, w, w^3, w^6, w^6, w^3, w, w^6, w, w^5, w^6, w^4, 1, w^6, w^6, w^4, w^5, w^2, w^3, w^5, w^3, w^2, w^3, 0, w, 0, w, w^3, 1, w^5, w, w^6, w^6, w^2, 1, w^2, w^2, 1, w^2, w^2, 0, w^3, w^6, w^4, w^3, 0, w^4, w^3, 1, w^5, w^6, w^5, w, w, w^2, w^6, w^5, 0, 1, w^4, 0, w^5, w, w^4, w^2, 0, 0 ] [ 0, 0, 1, 0, 0, 0, w^2, w^6, w^2, 1, w^5, w^5, w, 1, w^5, w, w^2, 0, w, w^6, 1, 0, 1, 0, w^4, w^6, 0, w^2, w^3, w^6, w, 1, w^5, w^3, w, w^6, w^5, w^3, w^5, w^5, 1, w^6, w^5, w^2, w^2, w^4, 1, w^2, w^2, w^6, 1, w^6, 1, w^5, w^5, 0, 1, w, 1, w^5, w^6, 1, w^6, w^4, w^4, w^5, w^6, w^2, w^4, w^6, w^3, 0, w^6, w^2, w^3, 1, 1, w^6, w^3, w^4, 0, w^3, w^4, w^3, w, w^5, w^5, 1, w^3, w^2, w, w^2, w^6, w^6, w^5, 1, 0, w^2, 0, 1, w^2, w^5, 1, w, w^2, 0, w^4, w^6, w^5, w, w, w^2, w^5, 1, w^3, w^2, w^3, w^6, w^4, w^3, 1, w^6, w^2, w^4, w^2, 0, w, w ] [ 0, 0, 0, 1, 0, 0, 0, 1, w^6, 1, w^5, w^6, w^6, w^2, w^2, w, 0, w, w^3, w^3, w^3, 0, 0, w^2, 1, w, w^3, w^5, w^3, w^5, 1, 0, 0, w^5, w^3, 1, w^2, w^5, w^3, w^2, w^2, w^5, w^3, w^5, w, w^3, w^2, w^4, w, w, w, w^6, w, w, w^6, w^2, w^5, 0, 0, w, w^2, 1, 1, w^2, w, w^6, 1, 1, w^2, 0, w^2, w^5, 1, 1, w, 0, w^2, w^3, w^4, w^2, w^4, 1, w^2, w^4, w, w^2, w^4, w^2, w^5, w, w, 1, 0, 0, w^3, 0, w^2, w, w^3, w^5, w^6, w^3, 1, 1, w^2, w^3, w^5, w, w^6, w^2, w, 1, 0, w^3, 1, w, w^2, w^5, w^3, w^4, w^3, w^4, 0, w^6, w^3, w^6, w^4, w^4 ] [ 0, 0, 0, 0, 1, 0, w^2, 1, w^6, w^3, w^5, w^3, w^5, w^6, w, w^2, w^6, w^3, w^4, w^4, w^5, w^2, 1, 1, w^6, 1, 1, w, w^2, 0, w, w^2, w, w, w^3, w^4, w^4, w^6, w^5, w^4, w^2, w, w^4, w^4, 0, 0, w^6, 0, w^4, w^3, w^6, w^5, w^2, w^2, w, w^4, w^3, w^2, 1, 0, w^3, w^2, w^5, w^5, 0, 1, w^3, w, w^2, w, w^4, w^5, 0, 0, 1, w^5, 1, 1, w^2, w^2, w^6, 0, w^5, w^3, w^3, w^3, w^4, w^3, 0, w^5, w^4, w^2, w^4, w^6, w^4, w^3, w^2, 0, w^2, 0, w^3, w^3, w^6, w^5, w^6, w^3, w^4, w, w^3, w^3, w^6, 1, w^6, w^4, 1, w^2, 1, w^3, w^3, w^6, w^5, 0, 1, w, w^6, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 1, w^6, 0, w^2, w, w^4, w, w^4, w^2, w^3, w^6, w^2, w, w^5, w^5, w^4, w^2, 1, 1, w^2, 0, 0, w^3, w^6, 1, w^3, w^6, w^3, w^3, w, w^5, w^5, w^2, w^4, w^5, w^6, w^3, w^4, w^4, 0, 0, w^6, 0, w^5, w, w^2, w^4, w^6, w^6, w^3, w^5, w, w^6, 0, 1, w, w^6, w^4, w^5, 0, 0, w, w^3, w^6, w^3, w^5, w^4, 1, 1, 0, w^4, 0, 0, w^6, w^6, w^2, 1, w^4, w, w^3, w^3, w^4, w, 1, w^4, w^5, w^6, w^5, w^2, w^5, w, w^6, 1, w^6, 1, w, w, w^2, w^4, w^2, w^3, w^4, w, w^3, w, w^2, 0, w^2, w^5, 0, w^6, 0, w, w, w^2, w^4, 1, 0, w^3, w^2, 0, 1, 1 ] where w:=Root(x^3 + x + 1)[1,1]; last modified: 2008-12-29
Lb(128,6) = 103 is found by truncation of: Lb(129,6) = 104 MST Ub(128,6) = 108 follows by a one-step Griesmer bound from: Ub(19,5) = 13 is found by considering shortening to: Ub(17,3) = 13 is found by considering truncation to: Ub(16,3) = 12 Hi4
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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