lower bound: | 22 |
upper bound: | 24 |
Construction of a linear code [40,9,22] over GF(4): [1]: [40, 9, 22] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, w, 1, w, 0, w, w^2, w, w, w^2, w^2, 1, w, 0, w^2, w, w, w^2, w^2, 1, 1, 1, 1, w, 1, 1, w, 1, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, w^2, 1, 0, w, 1, 1, w, w^2, w, w, w, 0, 1, w, w, w^2, w, w^2, w, w, w^2, 1, w, w, 1, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, 1, w, 1, w^2, w^2, 1, w, w, 1, w^2, 1, w^2, 1, 1, w, w^2, w, 0, w, w, w, w, w, 1, 1, 1, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, w^2, w^2, 0, w, w, 1, 1, 1, w^2, w^2, 1, w, w^2, w^2, w^2, 0, w^2, w, w^2, w, w, w^2, 1, w, 1, w^2, w^2, w^2, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, w^2, w, 1, 0, w, 1, 1, 1, 1, w^2, 1, 1, 1, w, w, 1, 0, w^2, w^2, w^2, w^2, 1, w^2, w, 1, 1, w^2, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, w^2, 1, 0, 1, w^2, w^2, w, w, w, w, w^2, w, 1, w^2, 1, 1, w^2, w^2, w, 0, w^2, w, w, w, w^2, 1, w^2, 1, w^2, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, w, 0, w, 1, w^2, w^2, 1, w^2, w^2, 1, w^2, w^2, w, w, w^2, w, 1, w^2, 0, w, w, w, w^2, w, w, w^2, w^2, 1, w, w, w ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, w^2, w, w^2, w, 1, w, w, w^2, w, w, w^2, 1, 1, w, 1, w^2, w, w, w, w, w, w^2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, 1, w^2, w^2, 1, w^2, w, 1, w^2, 1, w^2, w, w^2, w^2, w^2, w, w, w^2, 1, 1, w, 0, 0, 0, 0, 0, 0, 0, 0, w^2, w ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2012-08-21
Lb(40,9) = 21 is found by shortening of: Lb(41,10) = 21 is found by truncation of: Lb(42,10) = 22 DaH Ub(40,9) = 24 follows by a one-step Griesmer bound from: Ub(15,8) = 6 is found by considering shortening to: Ub(10,3) = 6 GH
GH: P.P. Greenough & R. Hill, Optimal linear codes over GF(4), Discrete Math. 125 (1994) 187-199.
Notes
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