lower bound: | 118 |
upper bound: | 118 |
Construction of a linear code [160,5,118] over GF(4): [1]: [162, 5, 120] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, w^2, w, 0, w, 0, 0, 0, 0, 1, w^2, w, 0, w^2, w^2, w, 0, 0, 0, 0, w^2, 0, 1, w^2, 1, w^2, w^2, w, w, w^2, w^2, 0, w^2, 1, w, w, w, w, w^2, w, 0, 1, 1, 1, 1, w, w^2, 0, 1, w^2, 1, w, w^2, w, 1, 0, 1, w, w^2, w^2, 0, 1, w^2, 0, 1, w, 1, 0, w^2, 1, w, 0, w, 1, w^2, 1, w, 0, w, 1, w, 0, w^2, w, 0, w^2, w, w^2, 1, w^2, w^2, w^2, 1, w, w^2, 1, w, w^2, w^2, 0, 1, 0, w^2, w, w^2, 0, 1, 1, w, w^2, w, 1, 0, w^2, 0, 1, 1, w, w^2, w, 1, 0, 0, w^2, w, w, 1, 0, 1, w, w^2, 0, w^2, w, w, 1, 0, 1, w, w^2, 1, w, w^2, w^2, 0, 1, 0, w^2, w, 0, 0, 0, w, 1, 0, w, w^2, 1 ] [ 0, 1, 0, 0, w^2, w^2, 0, 0, w, 0, w^2, w, w, w^2, 1, w, w, w, 1, w, w^2, w, w, w, w, 0, w^2, w^2, w^2, 1, 1, 0, 1, w, 1, 1, 1, 1, 1, 1, w, w^2, 0, 1, w^2, 0, 0, 0, 1, w^2, 0, 0, w^2, w, 1, w^2, 0, 0, w, 1, 1, w^2, 0, w, 0, w^2, w, 0, w^2, 0, w, 1, 0, 1, w^2, 1, 0, w, 0, 1, w^2, 1, 0, w, w, w^2, 1, w, w^2, 1, w^2, 0, 1, w^2, w^2, w^2, 1, w^2, 0, w, 0, w^2, w^2, 1, w, 1, w^2, 0, 1, w^2, 0, 0, w, 1, w, 0, w^2, 1, w^2, 0, 0, w, 1, w, 0, w^2, 0, w, 1, 1, w^2, 0, w^2, 1, w, 0, w, 1, 1, w^2, 0, w^2, 1, w, w, 0, w^2, w^2, 1, w, 1, w^2, 0, w, w, w, 0, w, 1, w^2, 0, 1 ] [ 0, 0, 1, 0, w^2, 0, 0, w, w, 0, w^2, w, w^2, w^2, w^2, w^2, 1, w, 1, w, w^2, w^2, w, 0, w^2, w^2, w^2, 1, w^2, w^2, w, w, w^2, w^2, 0, w^2, w, 0, w^2, w, 1, 0, 0, 0, 0, w, w^2, 1, 1, 1, 1, w, 1, 0, 1, 0, w, 1, 0, w, 0, 1, w^2, 0, 1, w^2, w, w^2, 1, w, w^2, 1, 0, w, 1, 0, w, 1, 1, w^2, 0, w, 0, w^2, 1, w^2, 0, w, 0, w^2, w, 1, 0, 1, 0, w, w, w, w, 0, 1, w^2, w, w^2, 1, 1, 0, w, w^2, w, 0, 1, 0, w, w, w^2, 1, 0, 1, w^2, w, w^2, 1, 1, 0, w, w^2, w, 0, 1, 0, w, w, w^2, 1, 1, 0, w, w^2, w, 0, 0, 1, w^2, 1, 0, w, w^2, w, 0, 0, 1, w^2, 1, 0, w, w^2, w^2, w^2, w^2, 0, 1 ] [ 0, 0, 0, 1, 1, 1, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, w^2, w^2, w^2, w, w^2, 1, w^2, w, 0, 1, 0, w, 0, 0, 0, 1, 1, 1, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, w^2, w^2, w^2, w, w^2, 1, w^2, w, 0, 1, 0, w, 0, 0, 0, 1, 1, 1, w^2, w^2, w^2, 0, 0, 0, 1, 1, 1, w^2, w^2, w^2, w, w^2, 1, w^2, w, 0, 1, 0, w, w, w^2, 1, w^2, w, 0, 1, 0, w, w, w^2, 1, w^2, w, 0, 1, 0, w, w, w, w, w^2, w^2, w^2, 1, 1, 1, w^2, w^2, w^2, w, w, w, 0, 0, 0, 1, 1, 1, 0, 0, 0, w, w, w, w, w, w, w^2, w^2, w^2, 1, 1, 1, w^2, w^2, w^2, w, w, w, 0, 0, 0, 1, 1, 1, 0, 0, 0, w, w, w, w, w^2, 1, w^2, w, 0, 1, 0, w ] [ 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, 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, 1, 1, 1, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [160, 5, 118] Linear Code over GF(2^2) Puncturing of [1] at { 161 .. 162 } last modified: 2005-11-22
Lb(160,5) = 118 is found by truncation of: Lb(162,5) = 120 BKW Ub(160,5) = 118 follows by a one-step Griesmer bound from: Ub(41,4) = 29 follows by a one-step Griesmer bound from: 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
|