lower bound: | 99 |
upper bound: | 107 |
Construction of a linear code [171,11,99] over GF(3): [1]: [171, 11, 99] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 1, 0, 0, 2, 0, 1, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 0, 0, 1, 0, 1, 1, 0, 2, 2, 2, 1, 0, 2, 0, 0, 0, 1, 0, 0, 2, 0, 2, 2, 1, 0, 2, 0, 0, 1, 1, 2, 1, 2, 1, 2, 2, 1, 0, 2, 1, 1, 0, 1, 0, 2, 1, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1, 1, 1, 2, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 2, 0, 0, 1, 2, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 1, 0, 1, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 2, 2, 0, 0, 2, 0, 2, 0, 0, 1, 1, 2, 1, 0, 0, 1, 0, 2, 1, 2, 1, 0, 0, 1, 1, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 0, 1, 0, 2, 2, 2, 1, 1, 2, 2, 2, 1, 0, 1, 0, 0, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 2, 0, 1, 2, 0, 0, 2, 0, 1, 0, 1, 1, 1, 2, 1, 1, 0, 2, 2, 2, 1, 1, 1, 1, 2, 2, 0, 0, 2, 1, 2, 2, 0, 1, 2, 0, 1, 0, 1, 2, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 2, 0, 0, 2, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 2, 2, 0, 1, 2, 2, 0, 2, 1, 0, 1, 2, 1, 1, 0, 0, 0, 2, 2, 1, 0, 1, 1, 2, 0, 1, 2, 2, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 1, 1, 1, 2, 1, 0, 2, 0, 1, 0, 0, 2, 1, 1, 2, 1, 0, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 2, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1, 0, 2, 2, 0, 1, 2, 1, 1, 1, 2, 2, 1, 0, 2, 2, 2, 0, 1, 1, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 0, 1, 1, 1, 0, 2, 2, 0, 1, 0, 2, 0, 0, 2, 1, 2, 0, 0, 1, 1, 0, 1, 0, 2, 1, 2, 2, 2, 0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 2, 0, 0, 0, 0, 2, 0, 1, 0, 1, 1, 2, 2, 1, 2, 1, 0, 0, 1, 1, 0, 1, 1, 0, 2, 0, 1, 0, 1, 2, 1, 0, 2, 1, 2, 1, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 2, 1, 2, 1, 2, 0, 1, 2, 2, 0, 0, 1, 0, 1, 1, 2, 0, 2, 1, 1, 2, 1, 1, 2, 1, 0, 0, 2, 2, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 1, 2, 1, 0, 0, 2, 2, 2, 1, 0, 1, 1, 2, 0, 2, 0, 0, 2, 0, 0, 1, 1, 0, 1, 2, 1, 1, 2, 2, 2, 1, 0, 1, 0, 2, 2, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 2, 0, 1, 1, 1, 2, 2, 0, 1, 1, 0, 0, 1, 2, 0, 2, 1, 1, 1, 1, 0, 1, 1, 2, 2, 0, 2, 2, 0, 2, 1, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 1, 1, 1, 2, 0, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 1, 2, 1, 2, 2, 2, 0, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 1, 1, 0, 0, 2, 0, 2, 2, 0, 1, 1, 2, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2, 2, 1, 0, 2, 2, 1, 0, 1, 2, 0, 0, 2, 0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 1, 0, 2, 1, 2, 2, 0, 1, 0, 2, 1, 1, 2, 1, 1, 0, 2, 1, 0, 1, 1, 2, 1, 1, 2, 1, 1, 1, 0, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 1, 1, 2, 1, 0, 2, 0, 0, 1, 1, 1, 0, 1, 2, 1, 2, 2, 0, 2, 0, 2, 0, 0, 0, 1, 2, 2, 1, 2, 0, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 2, 0, 0, 0, 0, 2, 1, 1, 2, 2, 1, 2, 0, 0, 1, 2, 0, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 0, 1, 0, 0, 1, 1, 0, 1, 2, 0, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 0, 1, 1, 2, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 2, 2, 0, 0, 2, 2, 2, 1, 2, 2, 0, 0, 1, 1, 0, 0, 2, 0, 2, 1, 0, 2, 0, 2, 1, 2, 0, 1, 1, 1, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1, 1, 2, 1, 1, 1, 2, 0, 2, 0, 1, 2, 0, 0, 1, 0, 1, 2, 2, 1, 2, 0, 2, 1, 2, 0, 2, 2, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 1, 0, 0, 2, 0, 2, 2, 0, 2, 2, 1, 1, 0, 0, 2, 2, 1, 1, 1, 2, 2, 0, 2, 1, 1, 2, 0, 2, 1, 0, 0, 0, 1, 0, 2, 2, 0, 1, 1, 1, 1, 2, 0, 0, 2, 0, 2, 1, 1, 0, 1, 1, 0, 1, 0, 0, 2, 1, 1, 2, 0, 2, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 1, 1, 2, 2, 0, 1, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 0, 1, 0, 0, 2, 1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 2, 1, 1, 1, 1, 2, 0, 2, 2, 1, 2, 2, 2, 0, 0, 0, 2, 0, 0, 2, 1, 1, 0, 1, 1, 0, 1, 2, 0, 0, 0, 0, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 2, 0, 2, 1, 1, 1, 0, 0, 1, 0, 1, 2, 1, 1, 0, 0, 2, 2, 0, 2, 1, 1, 2, 2, 1, 1, 1, 2, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 1, 0, 1, 1, 0, 2, 0, 1, 2, 1, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 1, 0, 2, 2, 1, 2, 0, 1, 1, 1, 0, 2, 2, 2, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 2, 1, 0, 0, 2, 0, 1, 1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 2, 2, 1, 2, 0, 0, 1, 1, 2, 2, 0, 1, 0, 2, 0, 1, 0, 0, 1, 2, 1, 2, 1, 0, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 1, 1, 1, 0, 1, 2, 0, 2, 2, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 0, 1, 0, 0, 2, 1, 1, 0, 1, 0, 0, 2, 1, 2, 0, 1, 0, 0, 2, 1, 0, 2, 1, 2, 0, 0, 2, 1, 1, 2, 1, 1, 2, 2, 0, 0, 1, 0, 1, 2, 0, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2, 0, 2, 1, 1, 1, 2, 1, 2, 1, 0, 0, 2, 0, 2, 1, 0, 2, 1, 1, 2, 2, 1, 2, 2, 0, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 1, 0, 0, 2, 2, 0, 1, 0, 1, 0, 2, 2, 1, 0, 1, 1, 0, 1, 2, 1, 0, 2, 2, 0, 1, 0, 2, 0, 1, 1, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 1, 1, 0, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 1, 2, 0, 2, 0, 1, 0, 1, 0, 1, 1, 0, 2, 0, 1, 2, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 1, 0, 0, 0, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 0, 1, 0, 1, 1, 0, 0, 1, 2, 1, 0, 2, 2, 0, 2, 1, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 1, 1, 1, 2, 1, 0, 1, 2, 1, 0, 0, 1, 0, 2, 1, 1, 2, 1, 2, 0, 0, 2, 1, 0, 1, 2, 0, 0, 2, 2, 0, 1, 1, 1, 0, 2, 2, 0, 0, 0, 1, 2, 0, 2, 1, 1, 2, 0, 1, 0, 0, 2, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1 ] last modified: 2009-08-13
Lb(171,11) = 97 is found by truncation of: Lb(174,11) = 100 MTS Ub(171,11) = 107 is found by considering shortening to: Ub(169,9) = 107 is found by considering truncation to: Ub(168,9) = 106 Da2
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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