lower bound: | 97 |
upper bound: | 99 |
Construction of a linear code [136,6,97] over GF(4): [1]: [136, 6, 97] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w^2, w, 1, 0, 0, w, 1, w, 0, 0, w^2, w^2, w^2, w^2, w^2, w, w, 1, 0, w^2, w, 0, 1, 0, 1, w^2, 0, w^2, w^2, w, w, w, 1, 1, 0, 1, 1, 1, w, w, w^2, 0, w^2, 1, w^2, w, 1, w, w, 0, 1, w, 1, 1, 0, w^2, w, w, w^2, w, 0, 1, 0, 1, 1, 0, 1, w, w^2, 1, 1, 1, 1, w^2, 0, w^2, w, 1, w, w^2, 1, w^2, w^2, w, w, w, w, 1, 0, w, w, w, w, 0, w^2, 0, 0, 1, w, 0, w, w^2, w, 1, 1, 1, w, 1, w^2, 1, 0, w, 0, w, w, w, 1, w, 0, 0, 1, 0, 0, w^2, 1, w, w, w^2, 1, 1 ] [ 0, 1, 0, 0, 0, 0, w, w^2, w, 1, 0, 0, w^2, 1, w, 0, 0, w^2, 1, w^2, w^2, w^2, w, w, 0, 0, w^2, w, 0, 1, w, 1, w^2, 0, w^2, w^2, 1, w, w, 1, 1, 0, 0, 1, 1, w, w, w^2, w, w^2, 1, w^2, w, 1, 1, w, 0, 1, w, 1, w, 0, w^2, w, w, w^2, 0, 0, 1, 0, 1, 1, 1, 1, w, w^2, 1, 1, 1, 1, w^2, 0, w^2, w, w, w, w^2, 1, w^2, w^2, w, w, w, w, 1, 0, 0, w, w, w, 0, w^2, w^2, 0, 1, w, 0, w, 1, w, 1, 1, 1, w, w, w^2, 1, 0, w, 0, 0, w, w, 1, w, 0, w, 1, 0, 0, w^2, 1, 1, 0, 1, w^2 ] [ 0, 0, 1, 0, 0, 0, 0, w, w^2, w, 1, 0, w^2, w^2, 1, w, 0, 0, w, 1, w^2, w^2, w^2, w, 1, 0, 0, w^2, w, 0, w^2, w, 1, w^2, 0, w^2, 0, 1, w, w, 1, 1, w^2, 0, 1, 1, w, w, 1, w, w^2, 1, w^2, w, 1, 1, w, 0, 1, w, w^2, w, 0, w^2, w, w, 1, 0, 0, 1, 0, 1, 1, 1, 1, w, w^2, 1, w, 1, 1, w^2, 0, w^2, w^2, w, w, w^2, 1, w^2, 0, w, w, w, w, 1, w^2, 0, w, w, w, 0, w, w^2, 0, 1, w, 0, w, 1, w, 1, 1, 1, 0, w, w^2, 1, 0, w, 0, 0, w, w, 1, w, 1, w, 1, 0, 0, w^2, 0, 1, 1, w^2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, w, w^2, w, 1, 0, w^2, w^2, 1, w, 0, w, w, 1, w^2, w^2, w^2, 0, 1, 0, 0, w^2, w, w^2, w^2, w, 1, w^2, 0, 1, 0, 1, w, w, 1, w, w^2, 0, 1, 1, w, w, 1, w, w^2, 1, w^2, w, 1, 1, w, 0, 1, w, w^2, w, 0, w^2, w, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, w, w^2, w^2, w, 1, 1, w^2, 0, w^2, w^2, w, w, w^2, 1, 1, 0, w, w, w, w, 0, w^2, 0, w, w, w, 0, w, w^2, 0, 1, w, 1, w, 1, w, 1, 1, w, 0, w, w^2, 1, 0, w, 0, 0, w, w, 1, w^2, 1, w, 1, 0, 0, w, w^2, 1, w ] [ 0, 0, 0, 0, 1, 0, 1, 0, 0, w, w^2, w, 0, 0, w^2, w^2, 1, w, w^2, w, w, 1, w^2, w^2, w, 0, 1, 0, 0, w^2, 0, w^2, w^2, w, 1, w^2, 1, 1, 0, 1, w, w, w, w, w^2, 0, 1, 1, w^2, w, 1, w, w^2, 1, 1, w, 1, 1, w, 0, w, w, w^2, w, 0, w^2, 0, 1, 1, 0, 0, 1, w^2, 1, 1, 1, 1, w, 0, w^2, w, 1, 1, w^2, 1, w^2, w^2, w, w, w^2, w, 1, 0, w, w, w, w, 0, w^2, 0, w, w, w, 0, w, w^2, 0, 1, 1, 1, w, 1, w, 1, 0, w, 0, w, w^2, 1, 1, w, 0, 0, w, w, 0, w^2, 1, w, 1, 0, 1, 0, 1, w ] [ 0, 0, 0, 0, 0, 1, w, 1, 0, 0, w, w^2, w, 0, 0, w^2, w^2, 1, w^2, w^2, w, w, 1, w^2, w^2, w, 0, 1, 0, 0, w^2, 0, w^2, w^2, w, 1, w, 1, 1, 0, 1, w, 1, w, w, w^2, 0, 1, 1, w^2, w, 1, w, w^2, 0, 1, w, 1, 1, w, w^2, w, w, w^2, w, 0, 1, 0, 1, 1, 0, 0, w, w^2, 1, 1, 1, 1, w^2, 0, w^2, w, 1, 1, w^2, 1, w^2, w^2, w, w, w, w, 1, 0, w, w, w, w, 0, w^2, 0, w, 1, w, 0, w, w^2, 0, 1, 1, 1, w, 1, w, 1, 0, w, 0, w, w^2, w, 1, w, 0, 0, w, 0, 0, w^2, 1, w, 1, 0, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2007-08-03
Lb(136,6) = 96 is found by truncation of: Lb(140,6) = 100 BKW Ub(136,6) = 99 follows by a one-step Griesmer bound from: Ub(36,5) = 24 follows by a one-step Griesmer bound from: Ub(11,4) = 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
|