lower bound: | 76 |
upper bound: | 80 |
Construction of a linear code [96,6,76] over GF(8): [1]: [96, 6, 76] Linear Code over GF(2^3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, w^5, 0, 0, w^6, w^2, w, 0, w^3, w^4, w^5, 0, w^6, 1, 0, w^6, w^4, 1, w^3, w^3, 0, w^3, w^6, 0, 0, 1, w^6, w, w^3, w^5, w^5, 1, w^6, w^2, w^5, w^4, 0, w^4, w^4, w^2, w, 0, w, w^5, w, w^2, w^2, 0, w^3, w^3, w^6, w^3, w^2, 0, w^5, w^6, 1, w^4, 0, w, 0, w^5, w^4, w^5, w^4, w^5, w^2, w^2, w^6, 1, w, 0, w^6, 1, w^3, w^4, 0, 1, w, w^3, w^4, w^4, w^6, w^6, w^2, w^2, w^2, w^2, w, 0, w^5, w^5, w^3 ] [ 0, 1, 0, 0, 0, 0, 0, 0, w, w^2, 0, w, w^3, w^4, w^3, w, w^3, w^4, w, 1, w^4, w^3, 0, w, 0, w^2, w^4, w^2, w, w^4, w^6, w^3, w^4, w^4, 1, 0, 0, w, w^4, w, 1, w, w^6, w, w^3, 1, w^5, w^3, 0, w, w^5, w^2, 1, w^4, w^2, w^4, 1, w^3, w^2, w^4, w, w^6, w^6, w^3, 0, w^3, 1, w^5, w^4, 1, w^5, 1, w^3, w^2, w^2, 0, 1, w^6, w^6, w^4, w^5, w^2, 0, 1, w^2, w^6, w^3, w^6, 0, w, w^4, 1, w^6, w, w^5, w^4 ] [ 0, 0, 1, 0, w^5, 0, 0, w^6, 0, 1, w^6, 0, w^3, w^6, w^6, 1, w^2, w^4, 0, 0, w^4, 1, 1, w^3, w, w, w^3, 1, w^4, w^3, w^6, w^6, w^2, w^5, w, 0, w^5, 0, w^5, w^2, w^6, w^3, w^6, 0, w^5, w^3, w^3, w^5, 0, w^3, w^3, 0, w^5, 1, w^4, w^3, w^2, w^6, 0, w^6, w^4, 1, w^3, w^3, 1, w^6, w^2, w^6, w^2, 0, w^5, w^5, w^3, w^4, 0, w^5, w^3, w^4, w^4, w, 0, w, w^4, 1, w, 1, w, 1, w^6, w^5, w^4, 0, w^5, 1, w^4, w^3 ] [ 0, 0, 0, 1, w^4, 0, 0, 0, w^3, w^6, w^5, w^4, w^2, 0, w^4, w^5, w^2, w^4, w^5, w, w^2, 0, w^4, w^6, w^3, 0, 1, w^5, w^5, w^3, 1, w^5, w^2, 1, 0, w^2, 1, 1, w^4, 1, 0, w^3, w^5, 1, w^4, w^6, 0, w^2, 0, w^5, w^2, 1, w^6, 1, w^2, 0, w^5, w^5, w^2, 1, w^6, w, w^5, 0, w, 0, w, w^2, w^6, 1, w^2, w^3, w^4, w^4, w^5, w^2, w^3, 1, 1, 0, w^2, 0, w^5, 1, w^6, 1, w^5, w^4, w^6, 1, w^3, 0, w^3, 1, w, w^4 ] [ 0, 0, 0, 0, 0, 1, 0, 1, w^2, w^2, 1, w^3, w^5, w^2, w^3, w^6, 0, w^3, w, 1, w^6, w, w^4, 1, 0, w^5, w^4, 0, 0, w^2, w, w, 1, w^6, 0, w^2, w^5, w, w^3, w^6, w^5, w^6, w^3, 0, w^6, w^2, w^5, w^5, w^3, w^2, w^5, w^3, w^2, w^5, w^5, w, w^5, w^5, w^4, w^4, w^5, w^2, w^6, w^2, w^6, 0, w, w^3, 0, 1, w^3, w, w^4, w^2, w^6, w^4, 1, 1, w, w^6, 0, w^6, w^3, w^6, w, w^3, 0, w^5, w^2, 1, w^5, w^2, w^6, w^5, w, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, w^6, w^6, 0, w, w^4, w^6, w^3, w^2, 1, w, w^3, 0, w^2, w^3, w^5, 0, 1, w^4, w^5, 1, 0, w^2, w, w^3, 0, w^2, 1, w^6, w^4, w^3, w, w^2, w^4, w^2, w^3, 0, w^2, w^6, w^4, w^4, w, w^6, w^4, w, w^6, w^4, w^4, w^3, w^5, w^5, w^5, w^5, w^4, w^6, w^2, w^6, w^2, 1, w^3, w, 1, 0, w^3, w, w^4, w^2, w^6, w^5, 0, 0, w^3, w^2, 1, w^2, w, w^2, w^3, w, 1, w^4, w^6, 0, w^4, w^6, w^2, w^4, w, 1 ] where w:=Root(x^3 + x + 1)[1,1]; last modified: 2008-12-05
Lb(96,6) = 75 is found by truncation of: Lb(117,6) = 96 DaH Ub(96,6) = 80 follows by the Griesmer bound.
Notes
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