lower bound: | 96 |
upper bound: | 102 |
Construction of a linear code [144,9,96] over GF(4): [1]: [144, 9, 96] Linear Code over GF(2^2) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, w, 0, 1, 0, 0, w^2, 0, w^2, w, 1, 0, 0, 0, 0, w, w, w, w, w, w, w, w, w, w, w, 0, 0, w, 1, w^2, w, 0, w^2, w, 1, w^2, 0, 1, w^2, w^2, w^2, w, 0, 0, 1, 0, 0, 1, 0, 0, 0, w, w, w^2, w^2, 0, 1, 1, 0, w^2, 1, 0, w^2, w, w^2, w^2, w^2, w, w^2, 0, 1, w, w^2, w, 0, 1, w, w, 0, w, 1, w, 0, 1, 1, w^2, 0, w^2, 0, w, 0, w, w^2, 1, w, 1, w, 1, w^2, 1, w, w^2, w^2, 1, w, w^2, w, 1, 1, w, w, w^2, w^2, w^2, 1, w, w, 1, 0, w, 1, 0, w^2, 1, w, w^2, 0, 0, 1, w, w, w^2, 0, w^2, 0, 1, w, 1, 0 ] [ 0, 1, 0, 0, 0, 0, w, 0, w^2, 1, w^2, 0, 0, w, 1, 0, 0, 0, 0, w, w, 1, 1, 0, 0, 1, 0, 1, w, w, 0, w, w^2, 0, w, 1, w^2, w^2, w^2, 0, w^2, w, w^2, w^2, 0, w^2, w^2, w, 0, 0, w, w, w^2, w^2, w, 1, 0, 1, w^2, 1, 0, 1, w, w^2, 0, w, 1, 1, 1, 0, w, w^2, w, 0, w^2, 0, 1, 0, w, 1, 1, 1, 1, w^2, 0, 1, w, 1, w^2, 0, 1, 1, 1, 1, w, w, w, 0, 0, w, w, w, w, 0, 0, w, w, 0, 0, w, 0, 1, 1, w^2, 0, w, w, w^2, w^2, 1, 1, 0, 1, 0, w^2, w^2, w, w, w, w, w^2, w^2, 1, 0, 0, 0, 1, w, 1, w, w^2, w, 1, 0 ] [ 0, 0, 1, 0, 0, 0, 0, w, 1, w, 0, w^2, 1, w^2, 0, 0, 0, 0, 0, w, w, w, w, w, w, w, w, w, w, w, 0, 1, 0, 1, 1, 1, 1, 1, 0, w^2, w^2, w, 1, w, 1, w^2, w^2, w, w, w^2, w, 0, 0, w^2, 1, w, 0, 1, 1, w^2, 0, w, 0, w, w^2, 0, w, 0, w^2, 1, w^2, w^2, 1, w, w^2, 0, 1, 0, w, w^2, 1, w, 1, 1, 0, w^2, 1, w, 1, 0, 0, w, w, 0, 0, 0, 1, 1, 0, 0, w, w, 0, 0, 1, w, w^2, w, w, w, 1, 1, 0, 1, 1, 0, w, 0, 0, w, w, w, 0, w^2, w^2, 1, 0, w, w, 0, 1, w^2, w, w^2, 1, w, 0, 1, 0, 1, w^2, w^2, w, 0 ] [ 0, 0, 0, 1, 0, w, w, 1, 0, 1, 0, w, 0, w, 1, 0, 0, 0, 0, 1, 1, w^2, w^2, 0, 0, w^2, 0, w^2, 1, 1, 0, w^2, w^2, 1, w^2, w, w, 0, 1, 0, w^2, 0, 1, 1, w, w^2, w^2, 0, w^2, w^2, 1, 1, 0, 0, w, 1, w, w^2, w, 0, 1, 1, 0, w^2, w, w^2, w^2, 0, w^2, 0, 1, 1, w, w, 0, w, w, w^2, 0, w^2, w, w, 0, 1, 1, 0, 1, w^2, w, w^2, w, w^2, 1, 0, 1, 0, w^2, 1, w, w^2, w, 0, 1, w^2, 0, w^2, w, 1, w, 1, w, w, w, 1, 1, w, w, w, w, 1, w^2, w^2, w, 0, 0, 1, w^2, w, 1, 0, w, w^2, 0, w, w^2, 0, 1, w, w^2, 0, 1, 0, w^2, w ] [ 0, 0, 0, 0, 1, w^2, w^2, 0, 1, 0, 1, w^2, 1, w^2, 0, 0, 0, 0, 0, 0, 0, w, w, 1, 1, w, 1, w, 0, 0, 0, w^2, w^2, 1, w, w^2, w^2, 1, 0, 1, w, 1, 0, 0, w^2, w^2, w^2, 0, w, w, 0, 0, 1, 1, w^2, 0, w^2, w, w^2, 1, 1, 1, 0, w^2, w^2, w, w, 1, w, 1, 0, 0, w^2, w^2, 1, w, w, w^2, 0, w, w^2, w^2, 1, 0, 0, 1, 0, w, w^2, w, w^2, w, 0, 1, 0, 1, w, 0, w^2, w, w^2, 1, 0, w, 1, w^2, w, 1, w^2, 0, w^2, w^2, w^2, 0, 0, w^2, w^2, w^2, w^2, 0, w^2, w^2, w, 0, 0, 1, w^2, w, 0, 1, w^2, w, 1, w^2, w, 1, 0, w^2, w, 1, 0, 0, w^2, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, w, w^2, 1, 0, 1, w, w, 1, 1, 0, w^2, 1, 0, w, 0, w, 1, 1, 1, 1, w^2, w, w, 0, 1, 0, 1, w^2, w^2, w^2, w, w, 0, 0, 1, 1, w, 1, 1, 0, 0, w, w^2, 1, w, w, w^2, w^2, w, w, w^2, w^2, w, 0, 0, 0, 0, 1, w^2, w^2, 0, w^2, 0, 0, w^2, 1, w, w, w^2, w, 0, 1, 1, 1, 0, 0, 0, w^2, w^2, 1, 1, w^2, w^2, w, w, w, w, w^2, 1, 1, 1, 0, w, 0, 1, 1, 0, 0, w, w, w, 1, 1, 0, w, w, 1, w, w^2, 0, 0, w^2, w, 1, 1, 0, w^2, 1, w, 0, w^2, 1, w, 0, w, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, w, 1, w^2, w^2, w, w^2, 0, w^2, w^2, w, w^2, 1, 0, 0, 1, w^2, w^2, 0, 1, w^2, 0, w, w^2, 1, w, w^2, w^2, w, 0, 0, 0, 1, w^2, w, w, w, w, 1, w^2, w, 0, w, w^2, 0, w^2, w, w, 0, 0, w^2, w^2, w, w^2, 1, 0, 1, w, w, 0, w, 0, w, 1, w, 1, w^2, w, w, 0, w, w^2, w, w^2, 0, 1, w, 0, w^2, 1, w^2, 1, 1, w, w^2, 0, w, 0, 1, 0, w^2, w^2, w, w^2, 0, 1, w^2, 1, 1, w, 0, w, 0, 0, w^2, 0, w^2, w^2, w^2, w, w, w^2, w^2, w, w, 1, 0, 0, 0, 1, w, w^2, 0, 1, 0, w^2, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, w^2, w, w^2, w, 1, 1, 0, 1, w^2, w^2, 1, w^2, 0, 1, w, 0, w^2, w^2, w, w, 1, w, 1, w^2, 0, 0, 1, 0, 0, 1, w, w, w, w, 1, 1, w, 0, 0, w^2, w, w^2, w^2, w, w^2, 0, 1, 0, w^2, 1, w^2, 0, 1, 1, 1, w, 0, w^2, w, 0, w^2, 1, 0, w, w^2, 1, 0, w, w, 0, w^2, w^2, w, w, w^2, 0, w, w, 0, w^2, w, w^2, w, w, 0, w^2, 0, w^2, 1, w^2, 1, 0, 1, 0, w^2, 1, w, 1, 0, 0, 0, w, w, 0, w^2, 1, 1, w^2, 1, 1, w^2, 1, w^2, w, 0, 1, w^2, 0, 1, w^2 ] [ 0, 0, 0, 0, 0, 0, 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^2, w, w^2, w, w^2, w^2, 1, 1, w, 1, w, 1, w, 1, w, w, w^2, 1, w, w^2, 1, w^2, w^2, 1, 1, w, w, w, w^2, w^2, w^2, 1, 1, w, 1, w^2, w^2, w, w^2, w^2, w, w, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w, w, w, w, w, w^2, w^2, w^2, w^2, w, w, w^2, w, 1, w, w^2, 1, 1, w, w^2, w^2, 1, w, w, 1, w^2, 1, w^2, 1, w^2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, w, w^2, 0, 1, 0, w^2, w ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2010-01-04
Lb(144,9) = 94 is found by truncation of: Lb(148,9) = 98 MTS Ub(144,9) = 102 is found by considering shortening to: Ub(142,7) = 102 is found by considering truncation to: Ub(140,7) = 100 DM3
MTS: Tatsuya Maruta, Mito Takenaka, Maori Shinohara & Yukie Shobara, Constructing new linear codes from pseudo-cyclic codes, pp. 292-298 in Proc. 9th International Workshop on Algebraic and Combinatorial Coding Theory(ACCT) in Kranevo, Bulgaria, 2004.
Notes
|