lower bound: | 168 |
upper bound: | 174 |
Construction of a linear code [240,8,168] over GF(4): [1]: [241, 8, 169] 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, 0, 0, 1, 0, 0, w^2, w, 0, 1, 1, w, w, 0, w, 1, 0, w^2, 0, w^2, 1, w, w, 1, 1, 1, w^2, w, w^2, w, w, w^2, w, w^2, 0, w^2, 0, 1, w, w^2, w, 1, w, w^2, 0, w^2, 0, w^2, w, 1, 0, 1, 0, w^2, 0, 0, 1, w^2, w, 1, w, 0, 0, 1, 1, w^2, 0, 1, w^2, w^2, w, 0, w, w^2, 0, w^2, w, w^2, 1, w^2, 1, w, w, w, 1, 0, 0, w, w, 1, 1, 1, 0, w^2, 0, w, 0, w, 1, w^2, w, 1, w^2, 0, w, w, w, 1, 1, 0, w, 1, w, 1, w, w^2, 0, w^2, 0, w^2, w, w^2, w, 1, 0, 0, w, w^2, w, w, w, 0, w^2, 1, 1, 0, w^2, w, 1, 1, 0, w^2, 1, 1, 0, 1, w^2, w, 0, w^2, w^2, w, 0, w, w^2, w, 1, w^2, w, 1, 0, 0, 0, 1, 0, w, 1, 1, w^2, 1, w, 0, w, w^2, 0, w, 1, w, w, w^2, 0, w^2, w^2, w^2, 1, w^2, 0, w^2, w^2, 1, 1, w^2, 0, 0, 1, 0, w^2, w, w^2, w^2, 1, 0, 0, w, 0, w^2, 0, w, w^2, 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^2, w, w^2, w^2, w^2, 1, w, 1, 0, w, 1, 1, w^2, w, w^2, 1, 1, w, 1, 0, 1, w, w, w^2, w, w, 0, w^2, w^2, w^2, w^2, 0, w^2, 0, 1, 0, w, 1, w^2, 1, w^2, 1, w^2, 0, w, w^2, w^2, 0, w, 1, 1, w^2, 1, 0, w^2, 1, w, 1, 0, w, 0, w^2, 1, 0, 1, w, 1, w, 0, w^2, w, w, 1, w^2, 1, 0, w, 0, w^2, 0, w^2, 0, w, 1, 1, 1, w, 1, w, 0, w^2, w, w^2, w^2, 0, w, 0, 0, w^2, 1, 1, 0, 1, 1, w, w^2, w, w, 0, w, w, 0, 1, 0, w, w, w, 0, w, w^2, w, w^2, 0, w, w, 0, w^2, 0, w^2, 1, w, w, 1, 0, w, 1, w, 0, w^2, w^2, 1, 0, 0, 1, w^2, 1, 1, 0, w, 1, 0, 1, 0, 1, w, 0, w, 0, 1, 0, 1, w^2, w, 0, 1, w^2, 1, 0, w^2, w, 0, 0, w^2, w^2, w^2, w, 0, w^2, 0, w, w^2, 1, w^2, w^2, 1, w, 0, 1, w^2, w^2, w, 1, 0, 0, 1, 1, w^2, 0, 0, w^2, w^2, w^2, 1, 0, 1, w^2, 0, w, w^2, 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, 0, 1, 0, 1, w, w, 1, w^2, 1, 0, w^2, w^2, 1, 0, w^2, w^2, 1, w, 1, 1, 1, w, w^2, w, w, w, w, w, w, w, w, w^2, 1, w^2, w^2, w^2, w^2, 0, 0, w, w, w^2, w, w, w^2, 0, w, 0, w, 0, 0, w, w^2, 0, w, w, w, 0, w, w^2, 0, w, w, 0, 0, w, 0, w^2, 0, 1, w^2, w^2, 0, 0, 0, w, 1, 1, w, 0, 1, w^2, w, w, 0, 1, 1, 0, 0, 1, 1, w^2, 1, w^2, 1, w^2, w^2, w, 1, 1, w^2, 1, 1, 0, 1, w^2, 1, w^2, w^2, 1, w^2, 0, 1, 0, 1, w^2, w^2, 1, 1, 0, w, 1, 0, 0, 0, w^2, w^2, 1, w, 1, w, w, w, w^2, w^2, 0, 0, 1, w^2, 1, 0, w, w, 0, 1, w^2, w^2, 1, 0, w, 1, 1, w, w, 0, 1, 0, 0, 1, 0, 1, w^2, w^2, w^2, 0, w^2, w^2, 0, 0, w^2, w, 0, w, w^2, w^2, w^2, w, w, w^2, w, 1, 1, 1, w, w^2, w^2, w^2, w, 1, 1, 0, 1, w, w, w, w, w^2, 1, 1, 1, w^2, 0, w, w, w^2, 0, w^2, 0, 1, 1, 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, 1, w, 0, 0, w^2, w, 0, w^2, 0, 1, 0, 1, w, w, 1, w^2, w, w^2, 0, 1, 1, 1, 1, w^2, w, 0, w^2, 0, w, 1, w, w^2, w, w, 1, 1, w, 1, 1, 1, w, 1, 1, w^2, 0, w, 0, 1, w, w^2, w, 1, w, 0, w, w, w^2, w, 0, w^2, w, 1, w, 0, 1, 1, w, 0, 1, 1, w^2, w, 1, w^2, 0, 0, w^2, w^2, w^2, 1, 1, w, 0, w, w, 0, 0, w, 1, w, w, w^2, 0, 1, 1, 0, w^2, 1, w^2, w^2, 1, w, w^2, w, w, 0, 0, 0, w, 1, w, w, 1, 0, 0, 1, 1, w^2, 1, w^2, 0, w, 0, w^2, 1, 0, 1, w^2, 0, w^2, w^2, 0, w^2, w^2, 1, 0, w^2, 0, w^2, w, 1, 1, w, w^2, w^2, w^2, w, 1, 1, 1, w^2, 1, 0, w^2, w, w^2, w, w^2, 1, w^2, 1, w, w^2, 1, 0, w, w, w^2, w, w^2, 1, 0, w^2, w, w, 0, w, 1, 1, w^2, w^2, 1, w, w, w, 1, w^2, w, w^2, w, w^2, w^2, w^2, w^2, 0, 1, 0, 0, w^2, 1, w^2, 1, 0, w, 1, w, 1, 1, w^2, 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, 0, 0, w^2, w^2, 0, 0, 1, 1, 0, 1, 1, 0, 0, w^2, 1, w^2, w^2, 1, w, w^2, 1, 0, w^2, w, w^2, w, w^2, w, w^2, 1, w^2, 1, w^2, w^2, w, w, w^2, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, w, w, 0, w, w, 1, 0, 0, w^2, w^2, w^2, w^2, 1, 1, 1, w, 1, w^2, w, 1, w, 0, w, 1, w, w^2, w, w^2, w, w^2, 1, 1, 0, 0, 0, w^2, w^2, w, w, w^2, 1, w^2, 0, 1, w, w^2, w, w^2, w, 1, w, 0, w, w^2, 0, w, w^2, 0, w, w^2, w^2, 1, 1, w, 1, 0, w, 0, w^2, 0, 0, w^2, 0, 0, w, 0, w, w^2, 0, 0, 0, 1, w^2, 1, w, 0, 0, 0, 0, 1, w, w, 1, w, 1, w^2, 0, 1, 1, w, 1, 0, w^2, 0, 1, w, 0, 0, 1, w, w^2, 0, w, w, 1, w^2, w, w^2, 0, 1, w^2, w, 0, 1, w, 0, w, w, 0, w, w^2, 1, w^2, 1, w^2, w, w, 1, w, 0, w^2, 1, 0, 1, w^2, 1, 0, 0, 0, w, w, w^2, w, 1, w, w^2, 1, 1, 0, 0, 1, 0, 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, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, w, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w^2, w, w, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, w^2, w^2, w^2, w^2, w^2, w^2, w, w, w, w, w, 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^2, w, w, w, w, w, w, w, 1, 1, 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^2, w^2, w^2, w^2, w^2, w^2, w^2, w^2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 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, 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, 1, 0, 0, 1, w, w, w^2, w^2, 0, 1, 0, w, 1, w, 0, 1, 1, w^2, w^2, 1, w, 1, 0, w^2, w, 0, w, w, 0, 1, 0, 0, w, 1, w^2, 1, 1, w, w, w^2, 0, 1, 1, w, w^2, w^2, w, 0, 1, 0, w^2, 0, w, 0, w^2, 0, 1, 1, w, w^2, w^2, w, w^2, w^2, w, w, 1, 0, 0, w^2, w, w^2, w^2, w, w, 0, 0, w, w, w^2, w^2, 0, 0, w, w^2, w^2, 0, w, w^2, w^2, 0, 1, w, w, 1, 0, 1, 1, w^2, w, w, 1, 1, 1, 0, 1, w^2, 0, w, 0, w, 0, w^2, 0, w^2, w, 1, w^2, w^2, w, 1, w^2, w^2, w^2, w^2, 0, w, w, 0, w^2, 1, 1, w, 0, 1, 0, 1, w^2, 0, w^2, 1, w, 0, 1, 0, w, 1, w^2, w, w, 1, 0, 0, 0, 0, w^2, w^2, w^2, w, 0, 0, w^2, w, w^2, w^2, w, w^2, 0, 1, w^2, 0, w^2, w, w^2, 1, w^2, 1, 1, w^2, 0, w, 1, 0, w^2, w^2, 1, 1, w^2, 0, 0, 0, w^2, w, 1, w, w, 1, 0, 1, 1, w^2, w^2, w, 0, 0, w, w, 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, 1, 0, 0, 1, w, w, w, w, 1, 0, 1, w^2, 0, w^2, 1, 0, 0, w, w, 0, w^2, 0, 1, w, w^2, 1, w^2, w^2, 1, 1, 0, 0, w, 1, w^2, 1, 0, w^2, w^2, w, 1, 0, 0, w^2, w, w, w^2, 1, 0, 1, w, 1, w^2, 1, w, 1, 0, 0, w^2, w^2, w^2, w, w^2, w^2, w, w, 1, 1, 1, w, w^2, w, w, w^2, w^2, 1, 1, w^2, w^2, w, w, 1, 1, w^2, w, w, 1, w^2, w, w^2, 0, 1, w, w, 1, 0, 1, 0, w, w^2, w^2, 0, 0, 0, 1, 0, w, 1, w^2, 1, w^2, 1, w, 1, w, w^2, 0, w, w, w^2, 0, w, w, w, w, 1, w^2, w^2, 1, w, 0, 0, w^2, 1, 0, 1, 0, w, 1, w, 0, w^2, 1, 0, 1, w^2, 0, w, w^2, w, 1, 0, 0, 0, 0, w^2, w, w, w^2, 1, 1, w, w^2, w, w, w^2, w, 1, 0, w, 1, w, w^2, w, 0, w, 0, 0, w, 0, w, 1, 0, w^2, w^2, 1, 0, w, 1, 1, 1, w, w^2, 0, w^2, w^2, 0, 1, 0, 0, w, w, w^2, 1, 1, w^2, w^2, 0, w, 0 ] where w:=Root(x^2 + x + 1)[1,1]; [2]: [240, 8, 168] Linear Code over GF(2^2) Puncturing of [1] at { 241 } last modified: 2008-09-06
Lb(240,8) = 165 is found by truncation of: Lb(241,8) = 166 MTS Ub(240,8) = 174 is found by considering truncation to: Ub(237,8) = 171 DM4
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
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