lower bound: | 61 |
upper bound: | 67 |
Construction of a linear code [111,11,61] over GF(3): [1]: [111, 11, 61] 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, 1, 0, 0, 1, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 0, 0, 1, 2, 2, 1, 0, 2, 0, 1, 2, 2, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 1, 2, 1, 0, 0, 0, 1, 2, 2, 2, 1, 2, 2, 1, 0, 0, 0, 0, 2, 1, 2, 0, 2, 2, 1, 1, 2, 0, 0, 0, 1, 2, 1, 2, 1, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 2, 2, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 0, 0, 2, 1, 0, 0, 1, 0, 1, 2, 0, 1, 0, 2, 2, 1, 1, 0, 0, 0, 2, 2, 1, 2, 1, 0, 1, 2, 1, 1, 0, 0, 2, 2, 2, 2, 1, 2, 1, 1, 2, 0, 2, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 1, 2, 0, 1, 0, 1, 2, 2, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 2, 1, 1, 2, 0, 0, 2, 2, 2, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 2, 2, 1, 1, 0, 2, 1, 0, 1, 0, 2, 1, 2, 2, 1, 0, 2, 2, 0, 2, 2, 0, 1, 1, 2, 0, 2, 1, 0, 0, 1, 2, 0, 0, 2, 0, 1, 0, 1, 0, 2, 0, 0, 1, 2, 1, 2, 2, 0, 0, 1, 2, 2, 0, 2, 2, 2, 1, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 2, 2, 1, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0, 1, 2, 2, 0, 2, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 1, 2, 1, 2, 2, 1, 0, 2, 2, 2, 1, 2, 2, 1, 1, 0, 0, 1, 0, 1, 2, 2, 0, 1, 2, 1, 2, 0, 2, 1, 2, 2, 0, 1, 0, 2, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2, 0, 1, 2, 2, 2, 0, 2, 1, 2, 2, 2, 1, 0, 1, 0, 2, 2, 1, 1, 1, 0, 1, 0, 1, 0, 0, 2, 1, 2, 1, 1, 1, 0, 0, 1, 2, 1, 1, 2, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 2, 1, 1, 0, 2, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 0, 2, 1, 0, 0, 1, 2, 0, 1, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 1, 2, 1, 1, 2, 1, 0, 1, 2, 0, 2, 1, 1, 1, 0, 1, 0, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 0, 2, 2, 2, 1, 0, 1, 2, 1, 2, 0, 0, 0, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 2, 1, 2, 1, 0, 1, 2, 0, 0, 2, 0, 0, 1, 2, 0, 1, 0, 2, 1, 1, 0, 0, 2, 2, 1, 0, 2, 0, 0, 2, 1, 2, 1, 1, 0, 1, 0, 1, 0, 0, 2, 0, 1, 1, 1, 2, 1, 1, 0, 1, 1, 0, 1, 1, 2, 0, 2, 1, 1, 1, 0, 1, 2, 2, 1, 0, 2, 2, 0, 1, 1, 2, 2, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 2, 1, 1, 1, 2, 0, 1, 1, 2, 2, 2, 1, 1, 0, 0, 1, 0, 2, 2, 0, 0, 1, 1, 2, 1, 2, 1, 0, 1, 2, 0, 2, 2, 0, 2, 2, 1, 1, 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 2, 2, 0, 0, 1, 2, 2, 0, 2, 2, 1, 2, 1, 1, 0, 0, 2, 1, 2, 1, 1, 0, 0, 2, 1, 2, 1, 2, 0, 2, 0, 0, 1, 1, 2, 2, 1, 2, 0, 1, 1, 0, 2, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 1, 2, 1, 2, 1, 2, 0, 1, 2, 0, 1, 1, 1, 0, 0, 0, 2, 1, 2, 0, 2, 1, 1, 2, 0, 0, 2, 2, 0, 2, 1, 2, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 2, 1, 0, 1, 1, 1, 1, 2, 0, 1, 0, 1, 2, 2, 2, 2, 1, 0, 0, 1, 1, 0, 2, 1, 1, 0, 1, 0, 0, 2, 2, 1, 2, 1, 0, 2, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 2, 1, 0, 2, 2, 2, 2, 0, 1, 1, 2, 1, 2, 1, 2, 0, 0, 0, 1, 2, 0, 1, 0, 0, 0, 1, 2, 1, 1, 1, 0, 1, 0, 1, 2, 0, 2, 0, 0, 1, 0, 2, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0, 1, 2, 2, 0, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 0, 2, 2, 1, 0, 2, 2, 1, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 1, 0, 1, 0, 0, 1, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 1, 1, 2, 2, 1, 1, 1, 0, 0, 1, 2, 0, 1, 0, 0, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 2, 1, 2, 2, 0, 1, 0, 1, 2, 0, 1, 1, 1, 1, 1, 1, 2, 2, 0, 2, 0, 1, 2, 1, 1, 2, 2, 1, 2, 0, 1, 0, 0, 1, 2, 2, 2, 2, 0, 0, 1, 2, 1, 2, 2, 1, 0, 2, 2, 2, 2, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 0, 2, 1, 0, 1, 2, 1, 0, 1, 2, 2, 0, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 0, 2, 2, 1, 1, 2, 2, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 0, 0, 2, 1, 2, 1, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 1, 1, 2, 1, 2, 0, 0, 2, 1, 0, 1, 2, 2, 1, 0, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 2, 1, 0, 2, 2, 2 ] last modified: 2009-06-05
Lb(111,11) = 60 is found by shortening of: Lb(112,12) = 60 BZ Ub(111,11) = 67 is found by considering shortening to: Ub(109,9) = 67 BKn
BZ: E. L. Blokh & V. V. Zyablov, Coding of generalized concatenated codes, Probl. Inform. Transm. 10 (1974) 218-222.
Notes
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