lower bound: | 118 |
upper bound: | 123 |
Construction of a linear code [172,8,118] over GF(4): [1]: [172, 8, 118] 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^2, 0, 0, 1, w, w^2, 0, w, w, 1, 0, w, 1, 0, w, 0, w^2, w^2, 1, w^2, 1, 1, 0, 1, 1, 0, w^2, w, 0, 0, 1, w^2, 1, 0, w^2, 0, 0, 1, 0, 0, 1, 0, 0, 1, w^2, w^2, 1, w^2, 1, 1, 0, 0, w^2, 0, w, 1, 1, 0, w^2, 0, 1, 0, 1, w^2, w, w, w, w^2, 1, w^2, 0, 0, w, w^2, w, w, w^2, 1, w^2, w, 1, 0, 0, w^2, 0, 1, w^2, w, 1, w, 1, w, 1, 1, 1, w^2, w, 0, w^2, 0, 1, 1, w^2, 1, w^2, w, w, w, 1, w, 1, w, w^2, w^2, w^2, 1, 0, 1, 0, w^2, w^2, 0, 1, w, w, w^2, 0, w, 0, w^2, 0, 1, 1, w, w, 0, w^2, w^2, w^2, w^2, 1, 1, w, 0, 1, w^2, w^2, w^2, w, 0, 1, w, w^2, 0, 0, w, 0, w^2, 0, 1, 0, w^2, 0, w, 0, w^2, w ] [ 0, 1, 0, 0, 0, 1, 0, 0, w^2, w^2, 0, 0, 0, w, 1, w, 0, w, 1, w, w, w^2, 0, 0, 1, w, 1, 1, 0, w^2, w^2, w^2, 1, w, 1, w^2, 0, w^2, w, w, 0, w, w, 0, 0, w, 1, 1, 1, w^2, w^2, w^2, 1, 0, w^2, 0, w, 0, 1, w, w, 1, w, 0, w, 0, 1, w^2, 0, w, 0, w^2, w, w^2, 1, w^2, w^2, 1, w^2, 1, w^2, 0, w, 0, 0, w, w^2, 1, 1, w^2, w^2, w, w, w^2, 1, w^2, 0, 1, w, 0, w, 0, 1, w, w, 0, w, 0, 0, w, 1, 1, w, 1, w^2, 1, 1, w^2, w, w, w^2, 1, 1, 1, w^2, 1, 1, 0, 0, w^2, w, 1, w, 0, 0, w, w, w, 1, w^2, 0, w^2, 0, w^2, 0, 1, w^2, w^2, w^2, 1, 1, w, w, 1, 0, 1, 1, w^2, w, w^2, 1, 1, 1, 1, 0, w^2, w, w, 1, w, w, w^2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, w, 0, 1, 0, 1, w^2, w, 1, 0, w, w^2, w^2, w, w, 0, 1, 0, w^2, 1, 0, 1, 1, 1, w^2, 1, 0, w^2, 0, w, w^2, w, w^2, 1, 0, w^2, 1, w, w^2, w^2, w^2, w, 0, w, w^2, 0, w^2, 1, w, 1, 1, 0, w^2, w^2, w^2, 0, w, w^2, w, 0, 0, 1, w, w^2, w^2, 1, w^2, 0, 0, w, 0, 0, 0, 1, w^2, w, 1, w, w, w, w, 0, 0, 1, w^2, 0, w, 1, w^2, w^2, w^2, 1, w^2, w^2, w, 0, w, w^2, w^2, 1, 0, 0, w^2, w, 1, 0, w^2, w, 0, 0, w^2, 1, 1, 0, 1, 0, w, 0, 1, w^2, w, w^2, w, w^2, w^2, w, 0, 1, w, w, w^2, 1, 1, w^2, w^2, 1, 1, 0, 0, 0, 1, w, 0, 0, 1, w^2, w^2, w, 1, 0, 0, 0, 0, w, w, w^2, 1, 0, w^2, 0, w^2, 1, w^2, 0, w ] [ 0, 0, 0, 1, 0, w, 0, 0, w^2, w, w^2, 0, 0, w^2, 0, 0, w, w, w, 1, w, w^2, w^2, 0, w, 0, w, w^2, w, 0, w, 1, w, 1, w, w, 0, w, 0, w, w^2, 0, w^2, w, w, w^2, 1, w^2, w, 1, w, w^2, 1, 1, 1, w, 0, 1, w^2, w, w, w, w, w, 0, w^2, 0, w^2, 0, 0, 0, 0, w, w^2, w, w, w^2, w, 1, w^2, w, 0, w, w^2, w, 0, w, w, 1, 1, w^2, 1, w, 1, 1, 1, 1, w, w, 1, w, w, 0, 0, w, w^2, w, w^2, 0, 0, w^2, 1, 1, 0, 0, w^2, 0, w, 1, 1, 1, 0, 1, 0, w^2, 1, 1, w, 0, w^2, 0, w, w, 0, 1, 0, 1, 1, 0, 1, w^2, w^2, w^2, 1, 1, 0, 0, 1, 0, w^2, w, w, 0, w, w^2, 0, w, w, 1, w^2, 1, 0, w, w, w, w, w^2, 1, w, w^2, w, w^2 ] [ 0, 0, 0, 0, 1, w^2, 0, 0, w^2, w, w, 0, w, w, 1, w, w, w, 0, w, w^2, 1, w, 0, 0, 1, w, 0, 1, 1, w, 0, w^2, 0, 1, 0, 0, w^2, 1, 1, w^2, 1, w^2, 0, 0, w^2, 1, 0, 0, w^2, w^2, 1, w, 0, w, w^2, 0, w, 1, 1, 1, 1, w, 1, 0, w, 1, w^2, 0, 0, 1, 0, w, 1, 0, 0, w^2, w, 1, 1, 0, w, 1, w, 0, w, 1, 0, w, w, w, w^2, w, w^2, 0, 1, w^2, w^2, 1, w, 0, 1, w^2, 1, w, w^2, 0, 1, w, 0, 0, 1, w^2, w, w, w^2, 1, 0, w^2, 1, 1, 1, 1, w^2, w, w, 0, 0, w^2, 1, w^2, 1, w, 1, 1, 0, 1, w^2, w^2, w^2, w, 1, 1, w^2, 0, 0, w, 0, 0, 0, 1, 1, w, w, w^2, 1, 0, w, 1, w^2, 0, 0, w^2, w, 0, 1, 0, w^2, w^2, w, w, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, w, 1, 0, w, w^2, w, 1, 0, 1, w, w, 0, w, 1, w, w, 1, 1, 0, w^2, w^2, w^2, w, 0, w^2, 0, w, 1, w^2, w^2, w^2, w^2, 1, 0, 1, w, w, 1, 0, w, 1, w^2, w^2, 0, 1, 1, 1, w^2, 0, w^2, w^2, w, 1, w^2, w^2, w, w^2, 0, w^2, w^2, w^2, 1, w, 1, 0, w^2, 1, 0, w^2, w, w, w^2, 0, w, 0, w, 0, w, w^2, 1, 0, w^2, 0, w, 0, w, w^2, 0, w, 0, 0, w, w^2, 1, 1, 0, 1, 1, w^2, 0, 0, 0, 0, 0, w, w, 0, w^2, w^2, w, 1, 1, 0, w, w, 0, w, w^2, 0, w, w^2, w^2, w^2, w, w^2, w^2, w^2, 1, w, w^2, 1, 0, w, 1, 0, 0, w^2, w, 0, w^2, 0, w^2, 0, 0, 0, w^2, w, 0, w^2, 1, w^2, 0, 1, 1, w, w^2, w, w, 0, 1, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 1, w^2, 1, 0, 0, w, w^2, w^2, 0, 1, 0, 1, 1, 0, w^2, 1, w^2, w^2, w^2, 1, w, 0, 1, 1, w^2, w^2, w, 1, 0, w^2, w^2, 1, w, 1, 1, w^2, 0, w, 1, w^2, 0, w^2, w^2, 0, w, 1, w^2, 1, w, w, 0, 1, 0, w^2, w, 1, w^2, w, 1, w^2, w^2, w^2, 0, w, 1, w, 1, w^2, 1, w, w^2, 1, 0, w^2, 0, 0, 1, w^2, w, w, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, w, w, 0, w, w, 1, w^2, 1, w, w, 1, w, 0, w, w, w, 0, w^2, w, w^2, w^2, w^2, 0, w^2, 0, 0, w^2, w^2, 0, 0, 1, 1, w^2, w^2, w, w, 0, w^2, w^2, 0, w, w^2, w^2, w, 1, w^2, 0, 1, 0, 0, w^2, 0, 1, w^2, 0, 0, 1, 1, w^2, 1, w^2, w^2, w, w^2, 0, 0, 0, w^2, 1, 0, 0, w ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1 ] where w:=Root(x^2 + x + 1)[1,1]; last modified: 2008-04-25
Lb(172,8) = 117 is found by taking a subcode of: Lb(172,9) = 117 is found by lengthening of: Lb(171,9) = 117 MTS Ub(172,8) = 123 is found by considering truncation to: Ub(171,8) = 122 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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