lower bound: | 84 |
upper bound: | 88 |
Construction of a linear code [124,8,84] over GF(4): [1]: [124, 8, 84] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 0, w^2, w^2, 1, 0, w^2, w^2, w^2, w, 0, 1, 0, 1, 1, w, w, 1, w, w, 0, 0, 1, 0, 1, 0, w^2, 1, 0, 0, 0, 1, w, w^2, 0, w, 1, w, w, w, 0, w^2, w, w, 1, w^2, 1, 0, 1, w^2, 0, w, 0, w, 1, 1, 0, w^2, w, w, w^2, w^2, 0, 1, w^2, 0, 0, w, w^2, 1, w, 1, 0, 1, w, w, 0, w^2, w^2, 1, 1, w^2, w, w, 0, 0, w^2, w^2, 1, w, 1, w^2, 0, w, 1, 0, 1, w, w^2, w, 1, 1, w, w, 1, 0, 1, w, 1, 0, w^2, w, 0, w^2, w^2, 0, w ] [ 0, 1, 0, 0, 0, 0, 0, w, 0, w^2, w, 0, w, w, 0, w, w^2, 0, 1, w^2, 0, 0, w, 0, w, w, 0, 1, w, 1, 0, w, w^2, w, w^2, w, w, w, w, 1, w^2, w, 1, w^2, w, w, 1, 1, 0, 0, w, 1, w, w^2, 0, 1, w^2, w, w, w, 0, 1, w, w, w, w^2, w, 0, w, 1, 0, w^2, 0, w, w^2, w^2, w, w, w, 1, w^2, 0, 0, 0, 1, w^2, w^2, w^2, 1, w, w, w, 0, w, 1, 0, w^2, w^2, w^2, 1, w^2, w, 0, w, w, 1, w, 0, w, w, 1, w, 0, w^2, 0, w, w, w, w, w^2, 0, 1, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, w^2, 1, 1, 1, 0, 1, 0, 1, w, 0, 0, 1, w^2, w, 0, w^2, 1, w, w, w, 1, 0, 1, w, w^2, 1, 0, 0, 0, 0, w, w^2, w^2, w, w, w^2, 0, w^2, w^2, 0, 0, 0, 1, w, w, w, w^2, 0, 0, w^2, w^2, 1, w, w^2, w, 1, w, 0, w, w^2, w^2, w, w, 1, 0, 0, w^2, 1, 0, 1, w^2, 0, w, 0, w, w, 1, w^2, w, 0, w, w^2, w^2, 1, w^2, w, w, 1, 1, 0, w^2, w^2, 0, 1, w, 0, 0, w, w, 1, 1, w, 0, 0, 0, w^2, w^2, 1, w^2, 1, 0, 1 ] [ 0, 0, 0, 1, 0, 0, 0, w^2, 0, 1, w^2, 1, w, 0, w, w, w, 1, w^2, 1, w, w^2, 1, w, w^2, 1, 1, w, 1, w^2, w^2, 0, 0, w, w^2, w^2, w, w^2, w, 0, 0, w, w, w, 1, w, w, w, 0, w^2, w, w, 1, w, w^2, 0, w, 0, 0, w^2, w, w^2, w^2, 0, w, 1, w^2, w^2, 1, w^2, w, 0, 0, 1, 0, 1, w^2, w^2, 0, w, 0, 1, 0, 0, 1, w, w, w, w^2, w^2, w, w, 1, 1, w, 1, 1, w, 1, w^2, w, 1, 1, 1, w, 1, w^2, w, 1, 1, w, w^2, 0, w^2, 1, 0, 0, 1, w^2, 1, 1, 0, 1, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, w, 0, 1, 0, 1, w^2, w, 0, w^2, 0, 0, 0, 0, w^2, w, 1, 0, w^2, w, w, 1, w, w, w^2, w^2, w, w^2, w^2, w, 1, w^2, w^2, 1, w, w, 0, 1, w, w, w, 1, w^2, 1, 0, w, 0, w, 0, w^2, 1, w^2, w, w, w, w^2, w^2, w, 1, w, 0, w^2, 1, 0, 0, w, w^2, 1, 0, 0, w, w^2, w, w, 0, 0, 1, w^2, w, w, w^2, 1, 1, 1, w, 1, 1, 0, w^2, w, 1, 0, 1, 0, w, w^2, w^2, w, w, w^2, 1, 0, w, w^2, 1, w^2, w, w^2, w, 0, 1, 0, w^2, w, 0, 1, w, w^2 ] [ 0, 0, 0, 0, 0, 1, 0, w^2, 0, 1, 1, w^2, 1, 1, w, 0, w^2, 1, 0, w^2, w^2, w^2, w^2, w^2, 0, 1, 0, w^2, w, 0, 0, w, w^2, w^2, 1, 1, w^2, w^2, w, w, w, w, 0, w^2, 0, w^2, 0, w^2, 0, w, w, w^2, w^2, 0, 0, 1, 0, 1, 0, 0, 1, w^2, 0, 1, w, 1, 1, 1, 1, 1, w^2, 1, w, 0, 1, w, 0, 1, 1, w^2, w^2, 0, w, 1, w, 1, 1, 0, w^2, 1, w, 0, 0, w, w, 0, 0, 1, w^2, 0, w, w, 1, w, w, 0, 1, w, 1, w, w^2, w^2, 0, w, w, 0, w, 1, w^2, 1, w^2, 1, 0, w ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, w, w, w, w^2, w^2, w, 0, w^2, w, w, 0, 1, w, 1, 1, w, 0, w, 1, w^2, 0, w^2, w, w^2, w^2, 0, 1, 0, 0, 1, w^2, 1, w^2, 1, 1, 0, w^2, w, w^2, w^2, w^2, 0, w^2, w, w, w, w, 1, 0, w^2, w^2, w, w^2, 1, w, 1, 1, w, w, w, 0, w^2, 0, 0, 0, 0, 0, w, w, w^2, 0, 1, 0, w, 1, w, w^2, w^2, 0, w, w^2, 1, 1, 0, 1, w, 1, w^2, w^2, w, 1, w^2, 0, 1, w, w, 1, 1, 1, 1, 1, 0, 1, 0, 1, w^2, 1, w, w, w, w, 1, w^2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, w, 1, 0, 1, 1, w^2, 0, w^2, w, w, 0, w, w, w^2, 0, w, 1, w, w, w^2, 0, w^2, w, w^2, w^2, w^2, w^2, 1, 1, 1, 0, w, 0, w, w^2, w, 0, 0, 1, 1, w^2, w^2, 0, 1, w^2, 1, 1, w^2, 0, 0, 1, w^2, w, 1, w, w^2, w, 1, w^2, 0, 1, w, 0, 0, 0, w, 0, 0, 0, 0, w^2, 1, 0, w, w^2, 1, 0, 0, 1, w, 1, 0, 1, w^2, w^2, w^2, w^2, w^2, 1, 0, w, 0, w, w^2, w^2, w^2, 0, w, w, 0, w^2, 0, w^2, 1, w, 0, 0, w, w^2, 0, w^2, w, w, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2010-04-28
Lb(124,8) = 83 is found by truncation of: Lb(125,8) = 84 BZ Ub(124,8) = 88 follows by a one-step Griesmer bound from: Ub(35,7) = 22 is found by considering shortening to: Ub(32,4) = 22 GH
GH: P.P. Greenough & R. Hill, Optimal linear codes over GF(4), Discrete Math. 125 (1994) 187-199.
Notes
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