lower bound: | 144 |
upper bound: | 150 |
Construction of a linear code [208,8,144] over GF(4): [1]: [208, 8, 144] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, w, 0, 0, 0, w, 0, 0, 0, 0, w, w^2, 0, w^2, 0, w, 0, w, 1, 0, 1, 1, 1, w^2, w, w^2, w, 0, 1, 1, w, 0, w, w, w, 0, w^2, 0, w, 0, 1, 0, w^2, w^2, 0, 1, w, 0, 1, 1, w, 0, 1, 0, w, 1, 1, w, 1, 1, w^2, w^2, 0, 1, 0, 1, 0, 0, w, w, w, w, w, w, 1, 1, 1, 1, 0, 0, 1, 0, w^2, w^2, 0, 0, w^2, w^2, w^2, 1, 1, 0, w, 0, w, 1, 0, 0, 1, w, 1, w^2, 1, w, 1, w^2, 0, w, w^2, 1, w^2, 1, w^2, 1, 0, w, 0, w, w, 1, 0, w, 0, 1, 0, w^2, w^2, 1, w, w, w^2, 0, w^2, 1, 1, 0, w^2, w, w^2, 1, w, 1, 1, 0, 1, w, 1, 1, 0, w, 0, w^2, 0, 0, 0, 1, 1, w, 1, 1, 1, 0, w^2, 1, w, w^2, 0, 1, 1, w^2, w^2, 1, w^2, w^2, 0, 1, 0, 1, w, 0, w^2, 1, w, w^2, 0, w, 1, w, w, w^2, w, 1, 0, w^2, 1, 0, 1, 1, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, w^2, 0, 0, 0, w, 0, 1, 0, w^2, w^2, 1, w^2, w^2, w^2, w^2, w^2, w, w, w^2, w, w, 0, w, w, w^2, 0, 1, 1, w, 1, 1, 0, w, w, 0, 1, w^2, 0, 0, w^2, 0, w^2, w^2, 0, w^2, 0, 0, w, 0, w, 0, w, w, 0, w^2, 1, w^2, 1, w, w, w^2, w, 0, w^2, w, w^2, w^2, 0, 1, w^2, w, w^2, 0, 0, w^2, w, w^2, 0, w^2, 1, w, 0, w, 1, 1, w^2, w, 1, w, w^2, 1, 0, w, 0, w^2, 0, w, 0, 1, 1, w^2, w, w^2, 1, 1, 1, 0, w^2, 0, 0, w^2, 1, w^2, w^2, w, 0, 0, w^2, w, 1, w^2, 1, w^2, 0, 0, w^2, 0, w, w^2, 0, w, 0, w^2, w^2, w, 0, w^2, w, w, w, 1, w^2, w^2, 0, w^2, 0, w, w, w^2, w^2, 1, 0, w, w, 0, 1, 0, 0, w^2, w^2, w, w^2, w, 1, 0, 1, 0, w, w, w^2, w, w, w^2, 0, w^2, w^2, w, 0, w, 1, 0, w, 1, w, w^2, 1, w^2, 0, 1, w, w^2, w, w, 1, 0, w^2, 0, 1, 0, w^2, w^2 ] [ 0, 0, 1, 0, w, 0, 0, 0, 0, 0, w^2, w, w^2, w^2, 0, w, 0, w^2, w^2, w^2, w^2, w, 1, w, w, 0, w^2, w, 0, w^2, 1, 1, w, 1, w^2, 0, 1, 1, 0, w^2, 0, w, 0, 1, 0, w^2, w^2, w^2, 0, 1, 0, w^2, 1, 1, 1, w, w^2, w^2, 1, 0, w, 1, w^2, w^2, w, w^2, 1, 0, 1, 1, w, w, w, 0, w^2, 0, w, w^2, w^2, 0, w, 1, 0, 1, w, 0, w, 0, w^2, 0, 1, 0, 0, w^2, w^2, 1, w^2, w^2, w^2, 0, 0, 1, 1, w, 1, 0, w, w, 1, w, w^2, 1, w, w^2, 0, 0, 0, w^2, w^2, 1, 0, w^2, 1, 0, w, 1, 0, w^2, w^2, 1, 0, w^2, 1, w^2, w, 0, 0, 1, w, 0, w, 0, w^2, w^2, w, w^2, w, 1, w^2, w^2, 1, w, w^2, 0, 1, w^2, 0, w^2, 1, 1, w, w^2, w, w^2, w, 1, 1, w^2, 0, 1, w, 0, w^2, 1, 1, w, 1, 0, 0, 1, 1, 0, w, 0, w, 1, w, 0, w, w^2, w, 1, w, w^2, w, 0, 1, w, 1, w, w, w, w, 0, w^2, 1, w, 0 ] [ 0, 0, 0, 1, w^2, 0, 0, 0, 0, 0, 0, w, 1, w^2, 1, w, 0, w^2, w^2, w^2, 0, w, w^2, w, w, 0, 0, 0, 0, w, w^2, w^2, 0, w^2, w, 1, 0, 1, w, w, 0, w, w, w^2, w^2, w^2, w, w^2, w, w^2, 1, 0, 1, 1, w^2, 0, 1, 0, 0, 0, 1, 0, w^2, w^2, 1, 1, 0, 1, w^2, w^2, w, w, w^2, 1, 1, w, 1, 1, w^2, 0, 1, 1, w^2, w, w^2, 1, w, 1, 0, w, w^2, w, w^2, w, 1, w, 1, w^2, 1, w, w, w, 0, w^2, 1, 0, 0, w, w^2, w, 0, w, 0, w^2, 0, 0, w, w, 1, 0, w^2, 0, w^2, w^2, 0, w^2, 1, w, 1, w, w, 1, w^2, w^2, w, 1, w, w^2, w^2, w, 1, 0, w^2, w^2, w^2, w^2, 1, w, w^2, 1, 0, 0, 1, 1, w^2, w^2, 0, 0, 0, w^2, 0, w^2, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, w, w, w, w, w, w, 0, 0, w, 0, 1, w, 0, 1, w^2, 0, 1, 1, w^2, w, w^2, 0, w, 1, w, 0, 1, 1, w, w^2, 0, w^2, w, w, 1, w ] [ 0, 0, 0, 0, 0, 1, 0, w, 0, 0, 0, w, 0, w^2, 0, 1, w, w, w^2, w^2, w^2, w, w^2, 1, w, 0, w, w, w, w, 1, w, 0, 1, w^2, 0, 0, 1, w, 0, w^2, 1, 0, 1, 1, 1, 0, w, w^2, w, 1, w^2, 0, w, w, 1, 1, 0, w^2, w^2, 1, 0, w, 0, 1, w, w^2, w^2, 0, w^2, 1, 1, w^2, w, 1, 1, 0, 0, 1, 1, w^2, 0, w^2, w^2, 1, 1, 0, 1, 0, w, w, w, w, w, 0, 1, w^2, 1, w, 1, 1, w^2, 1, 0, 1, 0, w^2, w, w, w^2, 0, 1, 0, w, w, w, 0, 0, 0, w, 1, w^2, w^2, w, w, 0, w^2, w, w^2, w^2, w, 0, 1, w, 1, w^2, w^2, 0, w, w, w, w, w, 0, 1, w, w, w^2, w, w^2, 1, 1, w, 0, 0, 1, w^2, 1, 1, w^2, w^2, w^2, 1, 1, w^2, w^2, w, w^2, 0, 0, w^2, w, 1, 0, 0, 1, w^2, w^2, w^2, w^2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, w, w, w^2, w^2, 0, 1, w^2, 0, w^2, w^2, w^2, w^2, 1, w, w^2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w, w, w, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w, w, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, w, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w, w, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, w^2, w^2, w^2, 1, 1, 1, 1, 0, 1, 0, w^2, w^2, w^2, w^2, w^2, w, 1, 1, 1, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, w, 1, 1, 0, w, w, 0, 0, 1, 0, 1, w, 0, w, w, 0, w, w^2, 0, w^2, 1, 0, 1, 1, w^2, w, 0, w, 1, 0, w, w, w^2, w, 1, 0, w^2, w^2, 1, 0, 0, 1, 1, 1, w^2, 0, w, w^2, w, w^2, 1, w, 1, 1, w^2, w^2, 0, 0, w^2, w, w^2, w, 0, 0, w, w, w, w, w^2, w^2, 0, 0, 0, 0, w, w, w^2, 0, w, w, 0, w, 0, 0, w^2, 1, 0, 1, w^2, w^2, w^2, w^2, w, 0, 1, w^2, w^2, w, w, w^2, w^2, w^2, w^2, 1, 0, 0, w, w^2, 0, w, w^2, 1, w, 0, w, w^2, 0, w^2, w, 0, w^2, w, 1, 0, 1, w^2, 0, w, 1, 1, w, w^2, 0, w^2, w, 1, 1, w, w^2, w, 0, 1, 0, 1, w^2, 1, w^2, w^2, 0, w, 0, w, w^2, w^2, w, w, 0, w^2, w, 1, 0, w^2, 0, w, 0, w^2, 1, 0, 1, 1, w^2, w, 1, w, 0, w^2, 1, 0, w^2, 0, w, w^2, w, 1, w, 1, w^2, w, 0, 1, 0, w^2, 1, w^2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, w^2, 0, 0, 1, w^2, w^2, 1, 1, 0, 1, 0, w^2, 1, w^2, w^2, 1, w^2, w^2, 0, w^2, 1, 0, 1, 1, w, w^2, 1, w^2, 0, 1, w^2, w^2, w, w^2, 0, 1, w, w, 0, 1, 1, 0, 0, 0, w, 1, w^2, w^2, w, w^2, 1, w, 1, 1, w, w, 1, 1, w, w^2, w, w^2, 1, 1, w^2, w^2, w^2, w^2, w, w, 1, 1, 1, 1, w^2, w^2, w, 0, w, w, 0, w, 0, 0, w, 0, 1, 0, w, w, w, w, w^2, 1, 0, w, w, w^2, w^2, w, w, w, w, 0, 1, 1, w^2, w^2, 0, w, w^2, 1, w, 0, w, w, 1, w, w^2, 1, w, w^2, 0, 1, 0, w, 1, w^2, 0, 0, w^2, w, 1, w, w^2, 0, 0, w, w^2, w, 0, 1, 0, 1, w^2, 1, w^2, w^2, 0, w, 0, w, w^2, w, w^2, w^2, 1, w, w^2, 0, 1, w, 1, w^2, 1, w, 0, 0, 1, 1, w^2, w^2, 0, w^2, 1, w, 0, 1, w, 1, w^2, w, w, 1, w^2, 0, w, w^2, 1, 0, 1, w, 1, w, 0 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2008-09-06
Lb(208,8) = 143 is found by shortening of: Lb(209,9) = 143 is found by truncation of: Lb(210,9) = 144 DaH Ub(208,8) = 150 is found by considering truncation to: Ub(206,8) = 148 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
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