lower bound: | 93 |
upper bound: | 94 |
Construction of a linear code [128,5,93] over GF(4): [1]: [131, 5, 96] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, w, w^2, 0, w^2, 0, w, 0, w, w^2, 0, w, 1, w^2, 0, 1, 1, w, w^2, 1, w^2, w, 0, w, 0, w, w^2, 0, 1, 0, 1, w^2, 0, 1, 0, w, w^2, 0, 1, 1, w, 1, 0, 1, w, 0, w, w^2, w, w^2, w, w^2, w^2, 0, 1, w^2, w, w^2, w, w^2, 0, 1, 1, 1, w^2, 0, 1, 0, w^2, 0, 1, w, w^2, 0, w^2, 0, 1, 1, w, w^2, 0, w^2, 0, 1, w, 1, 1, w, w^2, 1, w^2, 0, w, 1, 0, w, w^2, 0, w^2, 0, w, 1, 1, w, w, w^2, 0, w, 0, 1, w, w, w^2, w, w^2, w, w^2, 1, w, 1, 0, 1, w, 0, 0, 1, w^2, 0, 0, w^2 ] [ 0, 1, 1, 1, 0, 0, w, w, w^2, w^2, w^2, 0, 0, 1, 1, w^2, 0, 1, 1, 1, w, w, w^2, 0, 1, w, w, w, 0, 0, w, w, w, w^2, w^2, 0, 0, 0, w, w, w^2, w^2, 0, 1, 1, 1, w^2, w^2, w^2, 0, 1, w, w, w^2, 0, 1, 1, w^2, w^2, 0, 0, 1, 1, w^2, 0, 0, 1, 1, w, w, w^2, 0, 0, 0, 1, 1, w^2, w^2, 0, 1, 1, w, w, 0, 1, 1, w, w^2, w^2, w^2, 0, 1, w, w, w^2, 0, 1, 1, w, w, w^2, w^2, 0, 1, w, w^2, w^2, 0, 0, 1, 1, w, w^2, w^2, 0, 0, 1, 1, w, w, w^2, 0, 0, 0, 1, w^2, w^2, w^2, 0, 1, w ] [ 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, w, w, w, w, w, w, w, w^2, w^2, w^2 ] [ 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, 0, 0, 0, 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, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [128, 5, 93] Linear Code over GF(2^2) Puncturing of [1] at { 129 .. 131 } last modified: 2001-12-17
Lb(128,5) = 93 is found by truncation of: Lb(131,5) = 96 BDK Ub(128,5) = 94 follows by a one-step Griesmer bound from: Ub(33,4) = 23 is found by considering truncation 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
|