lower bound: | 63 |
upper bound: | 67 |
Construction of a linear code [96,8,63] over GF(4): [1]: [97, 8, 64] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 0, w^2, w^2, 1, 0, w^2, w^2, 0, 1, 1, 1, w^2, w^2, 0, 1, 0, 1, w, w, 0, 0, 1, w^2, 1, w, 1, 0, w^2, 1, 0, 0, w^2, w, w^2, 1, 1, 0, w, 1, 1, w^2, 1, 0, 0, 0, 0, 0, w^2, 0, w^2, w, w^2, w, 1, w, w, 0, w, 1, 0, w^2, 1, w, 1, w^2, 1, w, 1, w^2, w, w, 0, w, w^2, w, 0, 0, w^2, w^2, 1, 0, 1, 0, w, 0, 0, 1, 0, w ] [ 0, 1, 0, 0, 0, 0, 0, w, 0, w^2, w, 0, w, w, 0, w^2, w, 1, 1, w^2, w, 0, 0, w^2, 1, 1, 0, w, 0, w, w^2, w^2, w^2, 0, 0, 0, w, w, 1, w^2, w, 0, 0, 1, w, 0, 0, 1, 0, 0, 0, 1, 1, 0, w^2, 0, 1, 1, 0, 0, w^2, w, 0, 0, w^2, w, 0, 0, 1, w, w^2, 1, w, 1, w^2, w, 1, 0, w, w, w^2, 1, 1, w, w, 1, w^2, 1, w^2, 1, w, 1, w, w, 0, w^2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, w^2, 1, 1, 0, w, w, w^2, w, w, w, w^2, w, 1, w, w, 0, w^2, 1, 1, w^2, w, 1, 0, 1, 1, 0, w, w, 1, w, w, 0, w, 0, 0, 1, 1, 0, w^2, w^2, w^2, 0, w^2, 1, w^2, w^2, 0, w, 1, 0, 0, 1, w, 1, w^2, 0, w, w, w^2, 1, w^2, 1, w^2, 0, 1, w, 0, 1, 1, 0, 0, w^2, w^2, 0, 1, 0, 1, 1, w, w^2, w, 0, 1, w^2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, w^2, 0, 1, w^2, 1, w, 0, w, 0, 1, w, w, w^2, 0, 1, 0, w^2, 0, 0, 0, 1, 1, 0, w^2, 0, 0, 0, w^2, 0, w, w^2, w^2, w^2, 1, 1, w^2, w, w^2, 1, 0, w, w, 1, w^2, 0, w^2, w, 1, w^2, 0, 0, w, w^2, 0, 1, w^2, 1, w, w, w^2, w, 1, w, w^2, 1, w^2, w, w^2, w, w, w, w^2, w^2, 0, w, w, w^2, w, 1, 0, 1, 0, 1, w, 0, 1, 1, w, 0, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, w, 0, 1, 0, 1, w^2, w, 0, 1, 0, 1, 0, w, 0, 1, w, 0, w, w^2, w, w, w^2, 1, 1, w^2, w^2, 1, w, w^2, w^2, 1, 0, w, 0, w^2, 0, 0, 0, 0, 0, 0, w^2, 0, w^2, 0, 0, 0, 0, w^2, w^2, w^2, 0, w, 1, 0, 1, 0, w^2, w, 1, w^2, w, 1, w, w^2, 0, 1, w, 0, w^2, 0, 1, w^2, 0, 1, w, 1, w, w^2, w, w, w^2, w, w^2, w, w, w, w, w, w^2 ] [ 0, 0, 0, 0, 0, 1, 0, w^2, 0, 1, 1, w^2, 1, 1, w, 0, 0, 0, w^2, w^2, 1, w^2, w, 1, w, 1, 0, 1, w^2, w^2, w, w^2, 1, w, 1, w^2, 1, w, w, w, 1, w^2, 1, 0, 1, w, 1, 0, w, w, 1, 0, w, w, w^2, w, w^2, w^2, 0, 1, 0, w, w, 1, 0, w^2, 0, w^2, 1, 0, w, 0, w, w^2, 0, w, 0, w, 1, 1, 0, 0, 0, 0, 0, w, 0, w^2, w, w^2, w, 1, 0, w^2, 1, w^2, w ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, w, w, w, w^2, w^2, w, w, w, w^2, w, 0, 1, 0, 1, w^2, w^2, w^2, 1, w^2, w^2, w, 0, 0, 1, w^2, 0, w, 1, 0, w, 1, 0, 0, 0, 0, 1, w, w, w, 0, 0, w^2, 0, 0, w, w^2, w^2, w, w^2, w^2, w, w^2, w^2, 1, w^2, w^2, w, 1, w, 1, 1, w^2, 1, w^2, w^2, w^2, 1, 1, 0, 1, 0, w, 0, w^2, w^2, w^2, w, w, 1, 0, w, 0, 1, w, 0, w^2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, w, 1, 0, 1, 1, w, w^2, w^2, 0, 0, 1, w^2, 0, w^2, w, 0, w, 1, w, 1, w^2, 0, w^2, 0, w, w^2, w, w, 1, 0, 0, 1, 0, 1, 1, 0, w^2, w, 1, w^2, 0, 1, w^2, 1, 1, w^2, w^2, w, w, 0, w, 1, w^2, w^2, 1, w^2, 0, w, w, 1, w, w^2, 0, 0, 0, w, w^2, w^2, 0, w^2, w, 1, 1, w, 1, w^2, 1, 1, 0, w, 0, w^2, 1, 0, 1, 1, 1 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [96, 8, 63] Linear Code over GF(2^2) Puncturing of [1] at { 97 } last modified: 2009-01-27
Lb(96,8) = 62 is found by truncation of: Lb(98,8) = 64 DaH Ub(96,8) = 67 follows by a one-step Griesmer bound from: Ub(28,7) = 16 is found by considering shortening to: Ub(26,5) = 16 BGV
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
|