lower bound: | 69 |
upper bound: | 75 |
Construction of a linear code [108,9,69] over GF(4): [1]: [111, 9, 72] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, w, w^2, 1, 1, w^2, w^2, w^2, 0, w^2, 0, 0, 0, 0, w, 0, 0, w^2, w^2, 0, 0, 1, 0, 1, w, 1, w, 1, w^2, w^2, 1, w, w, 1, w, 0, w^2, w^2, 1, 0, 1, 1, w^2, w^2, w^2, w^2, w, 1, w^2, 1, 1, w, w^2, 0, w^2, 1, 1, 0, w, w^2, w, w, 0, w^2, w, 0, 1, w, w^2, w, w^2, w, w^2, w^2, 0, 1, w^2, 0, w, w, w, w^2, 0, w, w, 0, w, w^2, w, 1, w, 1, w^2, w^2, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w, w, 1 ] [ 0, 1, 0, 0, 0, 0, w^2, 1, 0, w^2, 0, 0, w^2, w, 1, 0, 1, 1, 0, w^2, 0, 0, 1, 1, 0, 0, 0, w, 1, 0, w^2, w, w^2, 0, 1, 1, 1, 1, w, 0, 1, w^2, 0, w^2, 1, w, 1, 0, 1, w^2, 1, w^2, 0, w^2, w, w, 0, 0, 1, w^2, w^2, 1, w, w, 0, 0, 1, w, w, 0, 1, w, 1, w^2, w^2, w^2, w, 1, 0, w^2, 0, 0, w^2, w, 1, 1, w, w^2, w^2, w^2, w^2, 1, 1, 0, w, 0, w^2, 1, w, 0, 1, w, w, w^2, 1, 0, 1, 0, w, w^2, 0 ] [ 0, 0, 1, 0, 0, 0, w, w, w, 1, 1, w^2, 0, w, w, 0, 0, 0, 0, w^2, 0, 0, w, 0, 0, w^2, w, w^2, 1, w, 1, 0, w^2, w^2, w, w^2, 0, 0, w, 1, w, 1, w^2, 0, 1, 0, 1, w, w, w^2, 1, 0, w^2, 0, 1, w^2, w, w, 1, 0, 0, w, w, w^2, 0, w, w^2, w, 1, w, w, w, w, 1, w^2, w, 1, 0, 0, 0, w^2, w, 1, w, w^2, 1, w, w, w, 1, 1, w^2, 1, 1, w, w, 1, w^2, 1, 1, w^2, 1, w^2, 1, w, w, w, w, w, w, 1 ] [ 0, 0, 0, 1, 0, 0, w^2, w, w^2, w^2, w^2, 0, 0, 1, w, 0, w^2, w^2, 0, w, 0, w^2, w^2, 0, 1, w^2, 0, 0, w^2, w, 1, w^2, w^2, w, 0, 1, 0, 1, 0, w^2, 0, w^2, w, 0, w, 0, 0, 1, 0, 1, w^2, w, 1, w, w, w, 0, w^2, 1, 0, 0, 1, w^2, 0, w, w^2, 1, 1, 0, w, 0, 0, 1, w, 1, w^2, w^2, w, 0, w, 1, w^2, w, 1, 0, w, 1, w, 0, w^2, 1, w, 1, 0, w^2, 1, 1, 1, w, 0, w, 1, w^2, 0, w^2, 1, w, w, 0, w^2, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, w^2, 1, 0, w^2, w, 0, w, w, 0, w^2, 0, 1, 1, 0, w, 1, 1, 1, w^2, 1, 1, w, w, w, w^2, w, w^2, w^2, w^2, w, w^2, w, w^2, w, w^2, 1, w, w^2, 1, 1, 0, 1, w^2, w^2, w, 1, w, w^2, 0, w^2, 1, 0, w, 0, 0, 0, w, 0, w^2, w^2, w, w, w^2, 0, 1, 0, 0, w, 0, w, w, 0, w^2, w, 0, 1, w^2, 1, 1, 1, w, w, w^2, 0, w^2, 1, 1, w^2, 1, w^2, w^2, 1, w, w^2, w^2, w, w^2, w, w^2, 1, 0 ] [ 0, 0, 0, 0, 0, 1, w, w^2, w^2, w^2, 1, 0, 1, w^2, 1, 0, 0, 0, 0, 0, 0, 0, w, w^2, 0, w, 0, w, w, w^2, w, w, w^2, 1, 1, w, w^2, w^2, 0, w^2, w, 1, w, 0, w, w^2, w^2, w, 1, w^2, w^2, 1, w, w, w, w^2, 1, 0, 1, w^2, 0, 1, w^2, w^2, 0, 1, 0, 1, w^2, 0, w^2, w, 0, w^2, w^2, 0, 1, 0, w^2, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, w, w, w, w^2, w^2, w^2, w, 1, 1, w, w^2, 1, w, w^2, 0, w^2, w^2, 0, w, w^2, w^2, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, w, 1, 0, w^2, 0, 1, w^2, w^2, w, w^2, w, 0, 0, w^2, 1, w, w^2, w^2, w, w, w, 1, 1, 0, w^2, w, w, w^2, 0, 0, 1, w^2, w, 1, 0, 0, w^2, 0, w^2, 0, w, w^2, w, w^2, 1, w, w^2, 1, w, w^2, 1, 0, w, 1, w, 1, w^2, 0, w^2, 0, 1, 0, w^2, w^2, 0, 1, 0, w, w^2, 0, w^2, 1, w^2, w, 0, w^2, 1, 0, 1, w^2, 0, 0, w^2, 1, w^2, 0, w, w, 1, 1, w, 1, 1, w, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, w, w^2, 0, w, 1, 1, w, 1, w, 1, 0, w, 0, w^2, 1, 1, 1, 0, w, w^2, 1, w^2, 1, 1, w, 1, 0, 1, 0, 1, w^2, w^2, 0, w^2, 1, 1, w, w, 1, w, w^2, 0, 1, w^2, 0, w^2, w, 0, w, 1, w^2, w^2, w, 1, w, 1, 0, w^2, w, w^2, 1, 0, 0, 1, w^2, 0, 1, w, w^2, w^2, w, w, 1, w, w^2, w, 0, 1, 0, w, w^2, w^2, w, 1, w^2, 1, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, w^2, 1, w, w, 1, 0, w, w^2, 1, w^2, w, w^2, 1, w, 1, 1, 0, w, w^2, 0, 1, w, w^2, w, w^2, 0, 1, 0, w^2, 0, w, 1, w, w^2, 1, w, 1, 1, 1, 0, 1, w^2, w, w^2, w^2, w, 1, 1, 0, 0, 1, w^2, 0, w, w, w^2, 1, w^2, 1, w, w^2, 1, w, 1, w^2, w, w, 0, 1, 0, w^2, 0, w^2, w^2, w, 0, w, 0, 1, 1, w^2, w^2, w, w, 1, 0, w^2, 0, 0, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [108, 9, 69] Linear Code over GF(2^2) Puncturing of [1] at { 109 .. 111 } last modified: 2010-04-28
Lb(108,9) = 68 is found by shortening of: Lb(113,14) = 68 DaH Ub(108,9) = 75 is found by considering shortening to: Ub(106,7) = 75 is found by considering truncation to: Ub(105,7) = 74 BK
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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