lower bound: | 112 |
upper bound: | 117 |
Construction of a linear code [164,8,112] over GF(4): [1]: [164, 8, 112] Linear Code over GF(2^2) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, w^2, 0, w^2, 0, w^2, w^2, w, 0, 1, w, 1, 0, 0, w, w^2, 0, 1, 1, 0, 1, w, 1, w, w^2, 1, 1, 0, 1, w, 1, 0, 1, 0, 0, 0, 1, w^2, 0, w^2, w^2, w^2, 0, w, w^2, 0, w^2, 0, w, w^2, w, 1, 1, w^2, w^2, 1, w^2, w, w^2, 0, 1, w^2, 0, 0, 1, w^2, w^2, w, w, w, 1, w^2, 0, 1, w, 1, 1, 0, w, w, 1, w, 0, w^2, w, 1, 1, 1, w^2, w^2, w, 0, 0, w^2, w, 0, w^2, 1, w^2, w, w^2, w, w, 1, w^2, 1, 0, w^2, 0, 0, w^2, 1, 0, w^2, w^2, w^2, 0, w^2, w, 0, 0, 0, w, 0, w, 1, 1, w, 0, w, w, w, w^2, 1, w, 1, w, 0, w, w, 0, w^2, 1, 0, 0, w, 1, w, w, 0, 1, w^2, w^2, w, 0, w^2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, w^2, 0, 0, 0, w, w, 1, w^2, w^2, w^2, 0, w, 1, w, w^2, w, w, 1, 1, 0, w, 0, 0, w, w^2, w, 0, 0, w, w^2, w, 0, 0, 1, 0, 1, w^2, 1, 0, w^2, 0, w^2, 1, w^2, w, w^2, 0, 1, w^2, 0, w, w^2, w, w, w, 0, w^2, 0, w, w, w^2, 1, w^2, 1, w^2, w, 1, 1, 0, w^2, 1, 1, w, w, 0, w^2, 1, w^2, w, w^2, 0, 1, 1, w, w, w^2, 0, w, w, 1, w^2, w, w^2, w, w^2, 1, 1, 0, w^2, 0, 1, 1, w^2, 1, 0, w^2, w, 0, w^2, w^2, 1, w^2, w, w^2, 0, w^2, 0, w, w^2, w, 0, w, 0, 0, 1, w^2, w^2, 1, 0, w, 0, 1, w^2, 1, 0, 0, 1, 0, w, w, 1, 1, w^2, 1, w, 1, 0, w^2, w, w^2, w^2, w, 1, w^2, 1, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, w^2, 0, 0, 0, w^2, w, 1, w^2, 1, w^2, 0, w, 1, w, w^2, w, w, 1, 1, 0, w, 0, 0, w, w^2, w, 1, 0, w^2, w^2, w, 0, 0, 1, 0, 1, w^2, 1, 0, w^2, 0, w^2, 1, w^2, w, w^2, 0, 1, w^2, 0, w, w^2, w, w, w, 0, w^2, 0, w, w, w^2, 1, w^2, 1, w^2, w, 1, 1, 0, w^2, 1, 1, w, w, 0, w^2, 1, w^2, w, w^2, 0, 1, 1, w, w, w^2, 0, w, w, 1, w^2, w, w^2, w, w^2, 1, 1, 0, w^2, 1, 1, 1, w^2, 1, 0, w^2, w, 0, w^2, w^2, 1, w^2, w, w^2, 0, w^2, 0, w, w^2, w, 0, w, 0, 0, 1, w^2, w^2, 1, 0, w, 0, 1, w^2, 1, 0, 0, 1, 0, w, w, 1, 1, w^2, 1, w, 1, 0, w^2, w, w^2, w^2, w, 1, w^2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, w, 0, w, w^2, 0, w, w^2, 0, w^2, w^2, 0, 1, 0, w, 1, 0, w, w^2, w, w, 1, 1, w, 0, 1, w, w, 0, w^2, 1, w, 0, 0, w^2, 1, 1, w, 0, 1, w^2, w^2, w, 1, w^2, w^2, 0, 1, w, 1, w, w^2, w, 0, w^2, 1, 1, w^2, w, w^2, w, w^2, w^2, w, 0, 0, 1, w, w^2, 1, w^2, w^2, w, 0, 0, 0, 0, w, 1, 1, w^2, 1, w, w^2, 0, 0, w, 1, 1, w, 1, w, 1, w^2, w^2, 1, 0, w, 1, w^2, w, w^2, 0, 1, 1, 1, w^2, w, 1, 1, w^2, 0, w, w^2, w^2, 1, 0, 0, w, w^2, 1, 0, 1, w, w, w, w^2, 0, w, w^2, w^2, w, w, 1, w, 0, w^2, w, 0, w^2, 0, 1, 1, 0, w^2, 1, w, 0, 1, w^2, w, 0, w, 0, w^2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, w^2, 1, w^2, w, 1, w, 1, 0, w^2, w^2, 1, w^2, w^2, w, w, 0, w^2, 0, 0, w^2, 1, w^2, 0, w, 0, w^2, 1, w^2, 0, w, 0, w, 1, w, 0, 1, 0, 1, w, 1, w^2, 1, 1, 0, w, 1, w^2, 1, w^2, w^2, w^2, 0, 1, 0, w^2, w^2, 1, w, 1, w, 1, w^2, w, w, 0, 1, w, w, w^2, w^2, 0, 1, w, 1, w^2, 1, 0, w, w, w^2, w^2, 1, 0, w^2, w^2, w, 1, w^2, 1, w^2, 1, w, w, 0, 1, 0, w, w, w, 1, 0, 1, w^2, 0, 1, 1, w, 1, w^2, 1, 0, 1, 0, w^2, 1, w^2, 0, w^2, 0, 0, w, 1, 1, w, 0, w^2, 0, w, 1, w, 0, 0, w, 0, w^2, w^2, w, w, 1, w, w^2, w, 0, 1, w^2, 1, 1, w^2, w, 1, w, 0, 0, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, w^2, 1, w^2, w, 1, w, 1, 0, w, w^2, 1, w^2, w^2, w, w, 0, w^2, 0, 0, w^2, 1, w^2, 0, w, 0, w^2, 1, w^2, 0, w, 0, w, 1, w, 0, 1, 0, 1, w, 1, w^2, 1, 1, 0, w, 0, w^2, 1, w^2, w^2, w^2, 0, 1, 0, w^2, w^2, 1, w, 1, w, 1, w^2, w, w, 0, 1, w, w, w^2, w^2, 0, 1, w, 1, w^2, 1, 0, w, w, w^2, w^2, 1, 0, w^2, w^2, w, 1, w^2, 1, w^2, 1, w, w, 0, 1, 0, w, w, w, w, 0, 1, w^2, 0, 1, 1, w, 1, w^2, 1, 0, 1, 0, w^2, 1, w^2, 0, w^2, 0, 0, w, 1, 1, w, 0, w^2, 0, w, 1, w, 0, 0, w, 0, w^2, w^2, w, w, 1, w, w^2, w, 0, 1, w^2, 1, 1, w^2, w, 1, w, 0, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, w, 1, 1, 0, w, w, w^2, 0, 0, w^2, 1, 0, w, w, 0, w, w^2, w, w^2, 1, w, w, w, 0, w, w^2, w, w, 0, 0, 0, w, 1, 0, 1, 1, 1, 0, w^2, 1, 0, 0, 1, 0, 1, w^2, w, w, 1, 1, w, 1, w^2, 1, 0, w, 1, 0, 0, w, 1, 1, w^2, w^2, w^2, w, 1, 0, w, w^2, w, w, 0, w^2, w^2, w, w^2, 0, 1, w^2, w, w, w, 1, 1, w^2, 0, 0, 1, w^2, 0, 1, w, 1, w^2, 1, 1, w^2, w, 1, w, 0, 1, 0, 0, 1, w, 0, 1, 1, 1, 0, 1, w^2, 0, 0, 0, w^2, 0, w^2, w, w, w^2, 0, w^2, w^2, w^2, 1, w, w^2, w, w^2, 0, w^2, w^2, 0, 1, w, 0, 0, w^2, w, w^2, w^2, 0, w, 1, 1, w^2, 0, 1, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, w, 1, w^2, 0, w, w, w, 0, 0, w^2, 1, 0, w, w, 0, w, w^2, w, w^2, 1, w, w, w, 0, w^2, w^2, 0, w, 0, 0, 0, w, 1, 0, 1, 1, 1, 0, w^2, 1, 0, 0, 1, w^2, 1, w^2, w, w, 1, 1, w, 1, w^2, 1, 0, w, 1, 0, 0, w, 1, 1, w^2, w^2, w^2, w, 1, 0, w, w^2, w, w, 0, w^2, w^2, w, w^2, 0, 1, w^2, w, w, w, 1, 1, w^2, 0, 0, 1, w^2, 0, 1, w, 1, w^2, 1, 1, w^2, w, 1, w, 0, 1, 0, 0, 1, w, 0, 1, 1, 1, 0, 1, w^2, 0, 0, 0, w^2, 0, w^2, w, w, w^2, 0, w^2, w^2, w^2, 1, w, w^2, w, w^2, 0, w^2, w^2, 0, 1, w, 0, 0, w^2, w, w^2, w^2, 0, w, 1, 1, w^2, 0, 1, 0, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2002-10-21
Lb(164,8) = 111 is found by shortening of: Lb(165,9) = 111 is found by truncation of: Lb(171,9) = 117 MTS Ub(164,8) = 117 is found by considering truncation to: Ub(163,8) = 116 Da1
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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