lower bound: | 68 |
upper bound: | 68 |
Construction of a linear code [80,4,68] over GF(8): [1]: [80, 4, 68] Linear Code over GF(2^3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, w^2, 1, w^6, w^6, w^6, w^6, w^2, w^5, w^5, w^3, w^3, w^6, w^6, w^3, w^3, w^6, w^6, 1, 1, w^5, w^5, 1, 1, w^5, w^5, 1, 1, w, 0, 0, w, 1, 1, 0, 1, 1, w^3, w^3, 0, w^4, w^5, w^5, w^4, w^2, w^2, w^5, w^2, w^2, w^6, w^6, w^5, w^2, w^2, 0, 0, 1, 1, 0, 0, 1, 1, w^3, w^3, w^2, w^2, w^4, w^4, w^5, w^5, w^4, w^4, w^5, w^5, w^3, w^3 ] [ 0, 1, 0, 0, 1, w^6, w^4, w, w^4, w^6, 1, 0, w^4, w, w^4, w^5, w^2, w, w^2, w^6, 1, w^5, w^3, w^5, w^3, w^5, 1, w^6, w^2, 0, w^4, 0, w^2, w^4, w^2, w^3, 0, w^3, w^2, w^6, w^4, w^6, w^2, w^4, 1, 0, 1, w^3, 1, w^3, w^6, w^4, w^2, w^4, w^6, w^2, w^3, w, w^4, w^3, w^4, w, w^3, w^4, w^2, 0, w, w^6, w^5, w^4, w^2, w^6, w^2, w^4, w^5, w^4, w, 0, w^2, w^3 ] [ 0, 0, 1, 0, 1, 1, 0, 0, w^2, 0, w^2, w^2, 0, w^2, w^2, w^2, 0, w^4, w^4, w^4, 0, w^4, w^4, w^4, 0, w^2, w^2, w^2, w, w, w, w^2, w^5, w^5, w^6, w^5, w^5, w^2, w^5, w^5, w^2, w^6, w^2, w^6, w^4, w^4, w^5, w^4, w^4, w^2, w^4, w^4, w^2, w^5, w^2, w^5, w^4, w^5, w^5, w^5, w^4, w, w, w, w^4, w, w, w, w^4, w^5, w^5, w^5, w^4, w^2, w^2, w^2, w^4, w^2, w^2, w^2 ] [ 0, 0, 0, 1, 1, 1, w^4, w^4, w^4, 1, 1, 1, w, w, w, w^3, w, w, w, w^3, w^5, w^5, w^5, w^3, w^5, w^5, w^5, w^3, w^4, w, w, w, w^3, w^3, w^3, w^2, w^2, w^2, 1, 1, 1, 1, 1, 1, w^5, w^5, w^5, w^6, w^6, w^6, w, w, w, w, w, w, w^2, w^2, w^2, 1, w^2, w^2, w^2, 1, w^4, w^4, w^4, 1, 0, 0, 0, 1, 0, 0, 0, 1, w^4, w^4, w^4, 1 ] where w:=Root(x^3 + x + 1)[1,1]; last modified: 2004-02-22
Lb(80,4) = 68 Bra Ub(80,4) = 68 follows by the Griesmer bound.
Notes
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