lower bound: | 54 |
upper bound: | 58 |
Construction of a linear code [80,8,54] over GF(5): [1]: [80, 8, 54] Linear Code over GF(5) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 4, 0, 1, 4, 4, 3, 4, 1, 4, 1, 1, 2, 4, 0, 1, 0, 3, 3, 4, 0, 4, 0, 2, 2, 0, 3, 3, 3, 4, 1, 2, 4, 4, 1, 0, 1, 0, 4, 4, 2, 2, 0, 0, 0, 1, 2, 3, 1, 2, 1, 1, 2, 1, 0, 0, 0, 3, 3, 1, 3, 0, 0, 4, 1, 3, 2, 3, 0, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 3, 2, 3, 1, 1, 3, 0, 1, 1, 2, 2, 2, 1, 1, 0, 4, 1, 2, 0, 2, 1, 0, 0, 1, 1, 3, 2, 3, 1, 1, 1, 0, 3, 2, 1, 2, 1, 2, 3, 0, 0, 3, 2, 0, 2, 2, 4, 4, 0, 4, 0, 4, 3, 1, 3, 0, 0, 0, 4, 3, 2, 2, 0, 1, 4, 4, 4, 3, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 3, 3, 4, 1, 3, 4, 4, 4, 4, 0, 2, 4, 3, 1, 0, 0, 0, 4, 0, 2, 1, 2, 3, 3, 1, 2, 2, 1, 3, 3, 3, 4, 1, 0, 4, 0, 3, 0, 3, 1, 3, 3, 4, 1, 1, 0, 3, 2, 0, 0, 1, 1, 1, 1, 2, 0, 3, 0, 1, 2, 4, 0, 0, 4, 0, 2, 4, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 2, 2, 0, 0, 3, 1, 2, 1, 1, 0, 0, 0, 2, 3, 2, 4, 1, 1, 0, 3, 2, 4, 1, 4, 0, 1, 1, 2, 0, 1, 4, 1, 3, 1, 0, 2, 1, 3, 2, 4, 4, 0, 2, 0, 1, 1, 4, 1, 2, 2, 1, 4, 2, 3, 4, 1, 2, 3, 0, 0, 4, 0, 4, 0, 2, 0, 1, 3, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 4, 1, 4, 4, 2, 4, 2, 1, 3, 1, 2, 4, 1, 4, 3, 0, 4, 4, 0, 3, 2, 0, 3, 2, 3, 3, 3, 3, 4, 1, 4, 1, 4, 4, 4, 3, 3, 1, 2, 4, 1, 3, 2, 3, 0, 3, 4, 2, 3, 3, 3, 3, 3, 1, 0, 1, 1, 1, 2, 2, 3, 4, 4, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 4, 0, 2, 1, 3, 2, 2, 4, 1, 0, 4, 0, 3, 3, 1, 0, 2, 4, 3, 4, 2, 4, 4, 0, 2, 3, 2, 3, 0, 3, 4, 2, 4, 4, 3, 1, 4, 4, 3, 4, 4, 2, 2, 0, 4, 2, 1, 1, 4, 3, 2, 1, 3, 2, 4, 1, 4, 0, 4, 4, 4, 4, 1, 3, 2, 3, 1, 2, 1, 4 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 4, 0, 4, 1, 4, 1, 1, 0, 0, 0, 3, 1, 4, 0, 0, 3, 2, 3, 1, 0, 2, 4, 0, 4, 3, 3, 1, 2, 4, 0, 3, 0, 1, 4, 2, 3, 1, 2, 3, 3, 2, 1, 2, 3, 0, 4, 3, 4, 4, 2, 2, 0, 4, 2, 2, 3, 0, 1, 1, 3, 2, 2, 1, 2, 0, 0, 0, 2, 0, 3, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 4, 0, 1, 0, 4, 0, 1, 3, 4, 4, 1, 2, 2, 4, 3, 0, 0, 4, 3, 2, 0, 2, 3, 2, 2, 4, 3, 2, 2, 1, 2, 0, 1, 2, 2, 1, 2, 1, 3, 2, 4, 4, 3, 4, 1, 3, 1, 1, 3, 4, 3, 3, 2, 0, 2, 4, 0, 3, 1, 2, 4, 2, 1, 2, 2, 2, 3, 4, 3, 3, 2, 4 ] last modified: 2010-01-04
Lb(80,8) = 53 is found by truncation of: Lb(84,8) = 57 DaH Ub(80,8) = 58 Da7
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
|