lower bound: | 141 |
upper bound: | 147 |
Construction of a linear code [204,8,141] over GF(4): [1]: [207, 8, 144] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w^2, w, w, 1, w^2, 1, 1, 0, 1, 0, 0, 0, 1, w^2, w^2, 0, w^2, 0, 0, w^2, 0, 0, w, w, 1, w^2, 1, w^2, w^2, 0, w^2, 0, w, w, w, w^2, w^2, 0, 0, 0, 1, 1, w, 0, w^2, 1, w, 0, 1, w^2, w^2, 1, 0, w^2, 1, w, 0, 1, w, 1, 0, w, w, 0, 1, 1, 0, w^2, 1, w^2, w, 0, w, w^2, w^2, 1, 0, 0, w^2, 0, 1, 1, w, w^2, 1, 1, w^2, 0, 0, w, 0, 0, 1, 0, 0, w^2, w^2, w, w^2, 1, w, 0, 1, w^2, w^2, w, w^2, 0, w, 1, w^2, 1, w^2, w^2, w^2, w, w^2, 1, 1, w, w, w^2, w, w^2, 1, 1, w, 1, 0, w, w, w, 1, w^2, 0, 0, 0, 0, 0, 0, 0, w, 0, w, w^2, w, 1, 1, w, 1, 1, w^2, 0, w, 1, w, 1, w^2, w, 1, w, w, 1, 1, w, w, w, w^2, 0, 1, 1, w^2, w^2, 0, 0, w, 0, 0, w^2, 0, 1, w^2, 1, w^2, w, w, w^2, 0, 1, w^2, 0, w^2, 0, w, w, w, 1, 1, 0, 0, 1 ] [ 0, 1, 0, 0, 0, 0, w^2, 1, w^2, w^2, 1, 0, w^2, 0, 1, 0, 0, w, 0, 1, w^2, 0, w^2, 0, 0, 1, 1, 1, 0, 1, 1, 0, 0, w, 0, 1, w, w, 1, w, w, w, 1, w, w, 1, 1, 0, w, 0, 0, w, w, 0, w, w, 0, 0, 0, w^2, w^2, 1, 1, 1, 1, 0, 0, 1, 0, w^2, w, 1, 0, 0, 1, 0, w, w^2, 1, 1, 0, w, w, w^2, 0, 1, w, w, w, 0, w, w^2, w, 0, 1, 0, w^2, w^2, w^2, w, 0, w, 1, 0, w, 0, w^2, 0, w^2, 1, 1, w, w, 1, w, 0, 1, w^2, w, w, w, w, w, 0, 1, w^2, 1, w^2, w, 1, 1, 1, w^2, 1, 0, w^2, w^2, w, w, w, w, w^2, 0, w, w, 1, w, 0, 0, 1, 0, w^2, w^2, 0, 0, w, w, w^2, w, 0, w^2, w^2, 1, w^2, w, w, 0, w^2, 0, w^2, 0, w, 0, 1, w, 1, 1, w^2, w, w, w^2, 0, w^2, 0, w^2, 0, 0, 0, 0, w, w^2, 1, 0, 0, w^2, 1, 1, 1, w^2, w^2, 1, 0, w^2, 0, w, 1, w^2 ] [ 0, 0, 1, 0, 0, 0, w^2, 1, 1, w, 1, w^2, 0, w, 1, 0, 0, 1, w^2, w^2, w^2, 0, w, w^2, 0, w, 1, w, w, w, w, w^2, w, w, 1, w, 0, 1, 1, 1, w^2, w^2, 0, w^2, 1, 0, 1, 0, w, 0, w, 1, 0, 0, w^2, 1, 0, w^2, w, w, 0, w^2, 1, w^2, w^2, 0, 1, w^2, 1, w, w, w^2, w^2, w^2, 1, 1, w, 0, w, 0, 1, 0, w, w^2, 1, 0, w^2, w^2, w^2, w, w, 1, w, 1, w, w, w, 1, w^2, 0, 0, 1, w^2, w, w, 0, 0, w^2, 1, 0, w^2, w^2, w^2, 0, w^2, w, 1, 1, w^2, 1, 0, 1, w, 1, w, 0, 1, w, w^2, 1, 0, w^2, w, 1, w^2, w, 0, 1, 0, 0, 0, w^2, w^2, 1, 1, w, 1, w^2, 1, 1, 1, w, w, w^2, w, 1, 0, 0, 0, 0, 0, 1, 0, 0, w, 1, w, w^2, w^2, w, w, w^2, 1, 1, w, w^2, w^2, 0, w, 1, w, 0, 1, 0, w^2, 0, w, w, 0, 0, 1, 0, w, w, w^2, 0, w, 0, w, w, w^2, w^2, w, w, 0, 0, w^2 ] [ 0, 0, 0, 1, 0, 0, w^2, w^2, 1, w^2, w, 1, 1, w^2, 1, 0, 0, 0, w, 1, w^2, w^2, 1, w, w^2, w^2, 0, 1, 1, 0, w^2, 1, 0, w^2, 1, 1, w, w^2, w^2, w^2, 1, w^2, 1, w, 1, w, w^2, 1, 0, w^2, w^2, w^2, 0, 1, 0, 0, 1, 0, w, w, w, 1, w^2, 0, 0, 1, w, 0, 0, 1, w^2, 1, w^2, w, 0, 0, w, w^2, 0, 1, w^2, 0, 0, 0, w, 0, w, 0, w^2, 0, 0, w, w, w, w, w, w^2, 1, 0, w, 1, w, 1, 0, 0, 1, 0, w, w^2, 0, 1, w, w^2, 1, w, w, 0, 1, 1, w^2, 1, w, 0, w, w^2, 1, 0, 0, 1, 1, 0, 1, w^2, w^2, 1, w, 0, w, 0, 0, 1, w^2, w, w, 0, w, 0, 1, 1, w^2, w^2, w^2, w^2, 1, 0, w, 1, 0, w^2, w, 0, 1, w, 0, w^2, w, 0, w, w, 0, w, w^2, w, 0, w, w^2, 0, w^2, w, 1, 0, 0, 1, w^2, w, w, 0, 0, w^2, w^2, 0, 1, 0, 0, 0, w^2, w^2, 1, 1, 1, 1, 0, 0, w^2, 1, w, 1 ] [ 0, 0, 0, 0, 1, 0, 0, w, 1, 0, w, w, w, 1, 1, 0, 0, w, 0, w, w, 0, 0, 1, 0, 0, w, w^2, 1, 1, 0, w^2, w, w, w, 0, 0, 1, w^2, 0, 0, 0, w^2, w^2, 0, w, w, 1, w^2, 1, w^2, 0, w^2, w^2, 1, 1, 0, 1, 1, 0, 0, w, 1, w, 0, w^2, w, w^2, 1, 0, 0, w^2, 0, w, 1, 0, 0, w^2, w^2, w^2, w, 0, 1, w^2, 0, w^2, 0, w^2, w^2, w^2, 0, w^2, w^2, 1, 0, w^2, 1, w, 1, w, w^2, 1, 0, w^2, w^2, w^2, 1, 1, w^2, 0, 1, w^2, w^2, w, 1, w^2, 0, 0, w^2, w, w^2, w^2, w, w^2, w^2, 1, w^2, w, 1, w^2, w^2, w, 0, 1, 1, 1, w^2, 1, 1, 1, w^2, w^2, w^2, 1, w^2, 1, w, 0, w^2, w, 1, w^2, 1, 0, w^2, 0, w^2, w, w, 0, w^2, w, 1, 0, 0, w, w^2, w, 0, 1, 1, w, 1, 1, w, w^2, 1, 1, 1, w, w, 0, w^2, w^2, w^2, 1, 0, w^2, w^2, w, w^2, 1, w, 0, 0, w, w, w, w^2, 1, w^2, w^2, w, w, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 1, w^2, 0, 1, w^2, w^2, w^2, 0, 0, 0, 0, w, 0, w^2, w^2, 1, 1, 0, 1, 1, w^2, w, 0, 0, 0, w^2, w^2, w^2, w^2, 1, 1, 0, w, 1, 1, 1, w, w, 1, w, w, 0, w, 0, w, 1, w, w, 0, 0, 1, 0, 0, 1, 0, w, 0, w^2, 1, w, w^2, w, 0, 1, 1, w, 1, w^2, 0, 0, 0, w^2, w^2, w^2, w^2, 1, 0, w, 1, w, 1, w, w, w, 0, w, w, 0, 1, w, 0, w^2, 0, w^2, w, 0, 1, w, w, w^2, 1, 1, w^2, 1, 0, w, w, w^2, 0, w, 1, 1, w, w^2, w^2, w^2, w, w^2, w, 0, w, w^2, 0, w, w, w^2, 1, 0, 0, 1, w^2, 1, 1, 1, w^2, w, w, 0, w, 0, w^2, 1, w, w^2, 1, w^2, 1, 0, w, 1, w, w^2, w^2, 1, w, w^2, 0, 1, 1, w, w, w^2, 1, 0, 0, w^2, 0, 0, w^2, w, 0, 0, 0, w^2, w^2, 1, w, w, w, 1, 0, w^2, w^2, w, w, 0, w^2, 1, 1, w^2, w^2, w^2, w, 0, w^2, w^2, w^2, w^2, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, w^2, 1, w, 0, w, 1, 1, 1, w, 0, w, w^2, w, w^2, 1, w, 1, w, 0, 1, 0, w^2, w, 0, w^2, 1, 1, w, w, w^2, w^2, w^2, w^2, w, 0, w, 1, 1, 1, w^2, 0, 0, 1, 0, w, 1, w, w^2, 1, 1, 1, w^2, 1, w, 0, w^2, w, 0, w, w, w, 1, 0, w^2, 1, w^2, w^2, 1, w, 0, w, 0, w^2, w, 1, 1, 1, w, 0, 1, w, 0, 0, w, w^2, w, w, 1, w, 1, w^2, w^2, 1, w^2, 1, w, 0, 0, w^2, 0, w, w^2, w^2, 0, w^2, w^2, 0, w^2, w^2, w, w, 1, w, w^2, 1, w, w^2, 0, w^2, w^2, 1, w^2, 0, 1, w, 0, w^2, w^2, w^2, 1, 1, 0, 1, w^2, w^2, w, 1, 0, 0, 1, 1, w, w^2, w^2, 1, w, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, w, w, w, 1, w, 0, 1, w, w^2, w^2, w, 1, 1, 0, 1, 0, 1, 1, w, 1, 0, w, w, w^2, 1, 1, 1, 0, w^2, w^2, 1, w, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, w^2, 1, 1, 0, w, w, w, 1, 1, 0, w, w, 0, w, w, 1, w, w^2, w^2, 0, w, w^2, 0, w^2, 1, 0, 1, w, 0, w^2, 0, w^2, w, w, w, w^2, w^2, w, 1, w^2, 1, 0, w, 0, w, w^2, 1, 1, 0, w^2, w^2, 1, 1, w, 1, w^2, 1, w^2, w^2, 1, 1, w^2, w^2, 0, 1, 0, 1, w, w^2, 0, w^2, 1, w^2, w, w^2, w^2, 0, w, w^2, w, 1, w^2, 0, 1, 0, w^2, w^2, w^2, w^2, 0, 0, 1, w^2, w^2, 1, 1, 1, 0, w, w, w, w^2, w, w, w^2, 1, 1, 0, w, 1, 0, 0, w, 1, w^2, 0, 1, 1, 0, w^2, w^2, 1, 1, 1, w^2, 1, 0, 1, 1, w^2, 1, 0, 1, w, w, w, 1, 1, 0, w, w^2, 0, w^2, 1, w^2, 0, 0, 0, 0, 0, 1, w, w^2, w, 0, w^2, 0, 1, 1, 1, 1, 1, w, 0, w, w, w^2, w, w, 1, w^2, w, w^2, w, 0, w, 1, w^2, 0, 0, w, 1, w, 0, w, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [204, 8, 141] Linear Code over GF(2^2) Puncturing of [1] at { 205 .. 207 } last modified: 2009-02-02
Lb(204,8) = 139 is found by shortening of: Lb(205,9) = 139 is found by truncation of: Lb(210,9) = 144 DaH Ub(204,8) = 147 is found by considering truncation to: Ub(202,8) = 145 DM4
DaH: Rumen Daskalov & Plamen Hristov, New One-Generator Quasi-Cyclic Codes over GF(7), preprint, Oct 2001. R. Daskalov & P Hristov, New One-Generator Quasi-Twisted Codes over GF(5), (preprint) Oct. 2001. R. Daskalov & P Hristov, New Quasi-Twisted Degenerate Ternary Linear Codes, preprint, Nov 2001. Email, 2002-2003.
Notes
|