lower bound: | 116 |
upper bound: | 117 |
Construction of a linear code [160,6,116] over GF(4): [1]: [160, 6, 116] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, w^2, w, 1, 0, 0, 1, 0, 1, 1, 1, w, 0, w, w^2, w^2, w, w, 1, 0, 1, w, w, w^2, 0, 1, 1, 1, 0, 0, 0, w^2, w^2, 0, 0, w^2, w^2, 1, w^2, 0, w^2, w, 0, w, w, w^2, w, w^2, 1, 1, 0, w^2, 0, 0, w, w, 1, w^2, w, 0, w^2, 0, w^2, 0, 0, 0, 1, w^2, 1, w^2, w, w, 1, w, 0, 0, w, w, w, 1, 1, 0, 1, w, 1, 1, w, w^2, 0, 0, w^2, 1, w, w, w, 1, 1, 0, w^2, 1, w^2, 1, 1, w^2, 1, w^2, w, 0, w, w^2, 0, 0, w, 0, w^2, 0, 1, w^2, 1, 1, 0, 1, 0, w, w, w^2, 0, w^2, w^2, 1, 1, w, 0, 1, w^2, 0, w^2, 0, w^2, w^2, 1, w^2, 0, 1, 1, w^2, 0, 0, 1, w, 1, w, 0, w^2, w, w^2, w, 0, 1 ] [ 0, 1, 1, 1, 1, 0, 0, 0, 0, w^2, w, w, 0, w^2, w, 0, w^2, w, w^2, 0, 0, w, 1, 0, w^2, w^2, 1, 1, w^2, 0, 0, w, 0, 1, 0, w, 1, 0, w^2, w^2, w, 0, 0, 1, 0, w, 0, w^2, w, 0, w, 1, 0, 0, 1, 1, w, 1, w, w^2, w^2, w, 1, w^2, 1, w^2, w^2, w^2, w, 1, w, 1, w, w^2, w^2, w, w^2, w^2, 1, 1, 1, 0, w, w, w^2, 0, w, w, w, 0, 1, w^2, w, w^2, 0, 0, w, 1, w^2, 1, 0, w^2, 0, 0, w^2, 1, 0, w, 0, 1, w, 1, 0, w^2, w^2, w, 0, 0, 1, 0, w, 0, w^2, w, 0, w, 1, 0, 0, 1, 1, w, 1, w, w^2, w^2, w, 1, w^2, 1, w, w^2, 1, w, 0, w^2, w, w^2, 0, 1, 1, 1, 0, w, w^2, 1, 1, w, w^2, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 1, 0, w^2, w^2, w, w, 0, w, 0, w, w^2, 1, w, 0, w, 1, 1, 1, w, w^2, 0, w^2, 0, 1, w, 0, w^2, w, 1, 1, 1, 0, w, 0, w, w^2, 0, 0, w^2, w, w, w^2, w^2, 1, w, w^2, w^2, w^2, w, 0, 1, 0, 1, w^2, w, 1, 0, w, 1, w^2, 0, w^2, w, 0, 0, 0, 1, w, 1, 1, w^2, w^2, w, 0, w^2, w, 1, 0, 0, w^2, 1, w, w^2, w^2, 1, w, 0, w, w, w^2, 1, 0, w, w, w^2, 0, 1, w^2, w^2, 0, 1, w, 1, w^2, w^2, w^2, w, 0, w, 0, 1, w, w, 1, 0, 0, 1, 1, w^2, 0, 1, 1, 1, 0, w, w^2, w, w^2, 1, 0, w^2, w, 0, w, 1, w^2, w, 0, w, 0, w, w, w^2, w^2, 0, w^2, 0, w^2, w, 0, 1, w^2, w ] [ 0, 0, 0, 0, 0, 0, 1, 1, 0, w, w, 0, w^2, w^2, w, 1, w^2, 0, w, w, 0, w, 1, 0, w, w^2, 0, w, w, 1, w^2, 1, w^2, 1, 0, 1, w^2, 0, w, 1, 1, w^2, w, 0, w^2, w^2, w, 0, 1, 0, 0, w^2, w, 0, w^2, 1, 0, w^2, w^2, w, 1, w, 1, w, 0, 1, w, w^2, w^2, w^2, w, 0, 1, 0, 1, w^2, w, 1, 0, w, 1, w^2, 0, w^2, w, 0, 0, 0, 1, w, 1, 1, w^2, w^2, w, 0, w^2, w, w^2, 1, w, w, w, 0, 1, 0, 0, w^2, w^2, 1, 0, w, 1, w^2, 0, 0, w, w^2, 1, w, w, w^2, 1, 0, 1, 1, w, w^2, 1, w, 0, 1, w, w, w^2, 0, w^2, 0, w^2, 1, 0, 1, 1, w, 1, w^2, 0, 1, 1, 0, w^2, w^2, 0, 1, 1, 0, w^2, w^2, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, w, w^2, w^2, 1, w, w^2, 1, w, w^2, w, 1, 0, w, 1, w^2, 0, 0, w, w^2, 1, w, w, w^2, 1, 0, 1, w, 1, 0, 0, 0, 1, w^2, w, w^2, w, 0, 1, w, w^2, 1, w, 1, 0, w^2, w, w, 1, w^2, 0, 1, 1, w^2, 0, w, 0, w^2, w^2, w^2, 1, w, 1, w, 0, 1, 1, 0, w, w, 0, 0, 1, 0, w, 1, 0, w^2, 1, 0, 0, w, w^2, w, w^2, w, 1, 0, w, 1, 0, w, w^2, 0, w, w, 1, w^2, 1, w^2, 1, 0, w, 1, 0, 0, 0, 1, w^2, w, w^2, w, 0, 1, w, w^2, 1, w, 1, 0, w^2, w, w, 1, w^2, 0, 1, 1, w^2, 0, w, 0, w, w^2, 1, w^2, 1, w, w^2, w, 1, 0, 0, 0, 1, w^2, w, 1, 1, w, w^2, 0 ] [ 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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2008-07-29
Lb(160,6) = 114 is found by truncation of: Lb(162,6) = 116 BKW Ub(160,6) = 117 follows by a one-step Griesmer bound from: Ub(42,5) = 29 follows by a one-step Griesmer bound from: Ub(12,4) = 7 is found by considering shortening to: Ub(11,3) = 7 is found by considering truncation 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
|