lower bound: | 52 |
upper bound: | 52 |
Construction of a linear code [72,5,52] over GF(4): [1]: [72, 5, 52] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, w, w, 0, w, 1, 0, w^2, 1, 1, 0, w^2, 1, w^2, w, w, 0, 1, 0, 0, w^2, 1, 0, 1, w, w^2, w^2, w^2, w, 0, w^2, w^2, 1, w, w, w, w, w^2, w^2, w^2, 0, 1, w^2, 1, 0, w, 0, w, 1, w, w, w, 0, 0, 0, 0, w^2, w, w^2, 0, 1, 1, w, w^2, 0, w, 1, w^2, 0, 1 ] [ 0, 1, 0, w, w^2, 0, 1, w^2, 1, w, 1, w, 0, 0, w^2, w^2, w, w^2, w^2, w, 0, w^2, w, 0, 0, 1, w^2, 1, w^2, 0, 1, 1, w^2, w, w, 0, w^2, w^2, 1, 0, 0, w, w^2, w^2, 1, 0, 0, w, w^2, w, w^2, 0, 1, 0, 1, 0, 1, w, w^2, w, 0, 1, 0, 1, 0, 1, w, 1, 1, 1, w, w ] [ 0, 0, 1, w^2, w, 0, 1, w^2, w^2, 1, 0, 0, w^2, 1, 1, 0, w^2, 1, 0, w^2, 0, 1, 1, 1, w, w, w, 1, w^2, 0, 0, w, 1, w^2, 1, w, w, 0, w^2, 1, w^2, 0, w, 0, w^2, 1, w^2, 0, 1, w^2, 0, w, 0, w^2, w^2, 1, w, 0, w, 1, w, 0, w^2, w^2, 1, w, 1, w^2, 0, w, 0, w^2 ] [ 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1, w, w^2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2010-04-28
Lb(72,5) = 51 is found by shortening of: Lb(73,6) = 51 is found by truncation of: Lb(78,6) = 56 Hi Ub(72,5) = 52 follows by the Griesmer bound.
Notes
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