lower bound: | 160 |
upper bound: | 164 |
Construction of a linear code [224,7,160] over GF(4): [1]: [224, 7, 160] Linear Code over GF(2^2) Code found by Axel Kohnert and Johannes Zwanzger Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, w, w^2, 1, 0, w^2, 0, 1, w, w^2, 0, 0, 0, w, 1, 1, w, 0, 0, w^2, 0, w, 1, 0, 0, w^2, 0, 0, w, 1, 0, 1, w, w^2, 1, w^2, 1, w^2, 0, w, w^2, 0, 0, w, 1, w^2, 0, 0, w, 1, 1, 1, w^2, w, 1, w, w, w^2, 0, 1, w^2, w^2, 1, w^2, 0, w^2, 1, w, 0, 0, 1, w, 0, w^2, w, 0, w, w^2, w^2, 0, w^2, w^2, 1, w, 1, w, w^2, 1, 1, 0, 1, w^2, w^2, 1, w, w^2, 0, 0, 0, w^2, w, 1, 1, 0, w, w, w^2, w, w^2, 1, 1, 1, w, 0, 0, w^2, w, w^2, 1, w^2, w, w^2, w, 0, 0, w^2, w, w, w, w^2, 0, w^2, w^2, w, 0, w^2, 0, 1, 0, w, 1, 0, w, 1, w, w^2, 1, 1, w, 1, w^2, w, 1, w, 0, 0, w, 0, 0, 1, 1, 1, 0, 1, w, 0, w, w^2, 0, w^2, 1, w^2, 1, 1, w^2, 1, 1, w, 1, w, 1, 1, 0, w^2, w^2, 1, 1, w^2, w^2, w^2, w^2, 1, 1, 1, w^2, w^2, 1, 0, w^2, w^2, w^2, w^2, 0, 1, 1, 0, 0, 0, 0, w^2, 0, w^2, 1, 1, 0, 0, 0, 0, 0, 0 ] [ 0, 1, 0, 0, w^2, w, 0, 1, 0, w^2, 0, 1, 0, 0, w, 1, w^2, 0, 0, 1, w, w^2, 0, 0, 0, w, 0, 0, 1, w^2, 0, 0, w, 1, 0, w, w^2, 0, 0, w^2, 1, 0, w^2, w^2, w, w^2, w^2, 1, w, 0, w^2, w^2, 0, w, w^2, 1, w^2, 0, w^2, 1, w^2, w, 1, w, 1, w, 0, 0, w, w, 1, 1, 1, 0, 0, w^2, w^2, w^2, w^2, 0, w, w, 0, w^2, w^2, w, w, 1, 1, w, 0, 0, w, w, 1, 1, 0, 1, 0, 1, w^2, 1, 0, 1, 0, w^2, w, 1, 1, 1, 1, w, w, 0, w, 0, 0, 0, w^2, w, w, w^2, w^2, w^2, w, 1, w^2, w, w, 1, w, w^2, w^2, 0, w^2, 1, 0, w^2, w^2, 1, 0, w^2, 0, 1, w^2, 0, 1, 1, w^2, 1, 0, 1, w^2, 0, 1, 1, w, 1, 1, w^2, w^2, 0, 0, 0, w^2, w, w^2, 0, w, w, 1, 1, w^2, w^2, 0, 1, w^2, 1, w^2, 0, 0, w, 0, 1, w, 1, w^2, 1, w^2, w, w^2, w^2, w, 0, 0, 1, w, w, 0, 1, 0, w^2, w, 1, w, w^2, 0, w^2, 0, w, w^2, w, 1, 0, 0, w^2, 1, w^2, 0, 1, w, 1, w, 1 ] [ 0, 0, 1, 0, w^2, 0, w^2, 1, 0, 0, 0, 0, 0, w^2, w, 0, w^2, w, 0, 1, w, 0, 1, 0, w, 0, 1, 0, 1, w^2, w^2, 0, 1, 1, w, w^2, 0, w, w, w, w^2, w^2, 1, w^2, 0, w, w^2, w, 1, w, 0, 0, 0, w^2, w, 0, 1, 1, w^2, 1, 1, w, w^2, w, 0, 0, w, 0, w^2, 0, 1, 1, w^2, 0, 1, 1, w^2, 0, 1, w, 1, 0, 1, w, 1, 1, w^2, w, 1, w, 1, w^2, 1, w^2, w, 0, 1, 1, 1, 1, w, w, 1, w, 1, w, 0, w, w, w^2, w^2, 0, 0, 0, 0, 1, 1, 0, w^2, 1, 1, w^2, w^2, w^2, w^2, w^2, w, w, 0, w, w, 0, 0, 0, w, w, 1, 1, 1, 1, w^2, w^2, w, w, w, w, 0, 0, 0, w^2, w^2, w^2, w^2, 1, 1, w^2, w^2, w^2, w, 1, 1, w^2, w, 1, w^2, w^2, 1, 0, w^2, 0, 0, w^2, 1, 1, 0, w^2, w^2, 1, 1, 0, 0, w^2, 1, 0, w^2, 1, 0, w^2, 0, 0, w, w^2, w, 1, w, w, w^2, 1, w, 0, w, w^2, w^2, w, 1, w^2, w, 1, 0, 1, w^2, 1, 0, 0, w, 1, 0, w^2, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 1, w, 1, w, 0, 0, 0, 0, 0, 0, 0, 1, w^2, 0, 1, w^2, w^2, 0, w, w^2, w, 0, 1, 0, 1, 0, w, w, 0, 1, 0, w^2, w, 1, w^2, w^2, w, w^2, w^2, 1, w^2, 0, 1, 0, 1, w, 1, w^2, w, w, 1, 0, w, w^2, 0, w, 0, 0, w^2, w, w^2, 1, 1, w^2, 1, w, 1, w, w, 0, w^2, w, w, 0, w, w^2, 0, w^2, w, w^2, 0, w^2, 0, w, w^2, 0, w^2, 0, w, 0, w^2, w, 1, 0, 0, 0, 0, w, w, 1, w, 1, w, w^2, 1, 1, 0, 0, w^2, w, w, w, w^2, w^2, w, w, 0, 0, w, w, w, w, w, w^2, w^2, 1, w^2, w^2, 1, 0, 0, w, w, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, w, 1, 1, w, w, w, w, 0, 0, w^2, w^2, w, w^2, 0, 0, w, w^2, 1, w^2, w^2, 1, 0, 0, w^2, w^2, 0, w, w, w, 1, 1, w^2, w^2, w, 1, w, 0, 1, w, 0, 1, w^2, 0, 1, w^2, w, w^2, 0, w^2, w, w^2, 1, w, 0, w, 0, 0, 1, w, 0, 0, w^2, w, w^2, 1, w^2, 1, 1, w^2, 0, 1, w, w, w^2, 0, 1, 0, w^2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, w^2, 1, w^2, 0, 1, w^2, 0, 0, w^2, 1, 0, 1, w^2, w^2, 0, w^2, 0, 1, 1, 0, w, w^2, w, w, w, 0, 1, 0, w, 0, w^2, 1, 0, 1, w^2, 1, 0, 1, w, w^2, 0, w, w^2, 1, w^2, 1, w, w, w^2, w, w, w^2, 1, 1, w, 0, 0, w^2, 0, w^2, 1, w, w^2, w, 0, w^2, w, w^2, 1, 0, 0, 1, w, 0, w, w, 1, 0, 1, w^2, w^2, w^2, 1, 1, w^2, 0, 0, 1, 0, w, w, 0, w^2, w^2, w^2, w^2, w, 1, w, 1, 1, 0, 0, 1, w^2, w^2, 0, 1, w, 0, 1, w, w, w^2, w, 0, w^2, 1, 0, 1, w, w^2, w^2, 0, 1, 0, w, 1, w, w^2, 1, w^2, 1, 0, 0, w^2, 0, 1, w^2, w, 1, 0, w, 1, w, 0, 0, w, w, 1, 1, 0, 0, w, w, w^2, w, 0, 1, w, 1, 0, w^2, w^2, w, w, 1, 1, 0, 0, 1, w^2, w^2, 1, 0, w, w, w, w, w^2, w^2, w^2, w^2, w^2, w^2, 1, w^2, w^2, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, w^2, w^2, 0, w^2, 0, w^2, 0, 0, w, 1, w^2, w^2, w^2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, w, 0, w, 1, 0, w, 1, 1, w, 0, 1, 0, w, w, 1, w, 1, 0, 0, 0, w, w^2, w, w, w, 0, 1, 1, w^2, 1, w, 0, 1, 0, w, 0, 1, 0, w^2, w, 1, w^2, w, 0, w, 0, w^2, w^2, w, w^2, w, w^2, 1, 1, w, 0, 0, w^2, 1, w, 0, w^2, w, w^2, 1, w, w^2, w, 0, 1, 1, 0, w^2, 1, w^2, w^2, 0, 1, 0, w, w, w^2, 1, 1, w^2, 0, 0, 1, 1, w^2, w^2, 1, w, w, w, w, w^2, 0, w^2, 0, 0, 1, 1, 0, w, w, 1, 0, w^2, 1, 0, w^2, w, w^2, w, 0, w^2, 1, 0, 1, w^2, w, w, 1, 0, 1, w^2, 0, w^2, w, 0, w, 0, 1, 1, w, 1, 0, w, w^2, 0, 1, w^2, 1, w, 0, 0, w, w, 1, 1, 1, 1, w^2, w^2, w, w^2, 1, 0, w^2, 0, 1, w, w, w^2, w^2, 0, 0, 1, 1, 0, w, w, 0, 1, w, w, w, w, w^2, w^2, w^2, w^2, w, w, 0, w, w, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, w, w, 1, w, 1, w, 1, 1, w^2, 0, w, w^2, w, 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, 0, 0, 1, 1, w^2, w^2, 1, w, 1, w, 1, 1, w, w, w^2, w^2, w^2, 1, 1, w^2, w, w, w^2, w, w^2, w, 1, 1, w, w, 1, w^2, w^2, w, 1, w, 1, 1, 1, w, w, w^2, 1, 1, w^2, w^2, 1, 1, w^2, w^2, w, w^2, w^2, w, w, w, 1, 1, w, w, w, 1, 1, w, w^2, w, 1, w, w^2, w, w^2, w, 1, w^2, 1, w^2, w, 1, w^2, w^2, w, w, 1, w^2, w, w^2, 1, 1, w, 1, w, w, w^2, w^2, 1, 1, 1, w, w, w, 1, 1, w, 1, 1, w^2, w^2, 1, 1, w^2, w^2, 1, 1, w, w, 1, 1, w, w^2, w^2, w, w, w^2, w^2, w, w, 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, 0, 1, w^2, w^2, w, w, 1, w^2, w^2, 1, 1, 1, w^2, w, w, w^2, w^2, 1, 1, w, w, w^2, 1, 1, w^2, w, w, w, 1, w, 1, w^2, w^2, w, w^2, 0, 1, 0, w^2 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2008-07-29
Lb(224,7) = 159 is found by truncation of: Lb(226,7) = 161 MTS Ub(224,7) = 164 follows by a one-step Griesmer bound from: Ub(59,6) = 40 follows by a one-step Griesmer bound from: Ub(18,5) = 10 Liz
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
|