lower bound: | 123 |
upper bound: | 129 |
Construction of a linear code [204,10,123] over GF(3): [1]: [204, 10, 123] 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, 2, 1, 1, 0, 2, 2, 2, 1, 0, 1, 2, 2, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 0, 2, 1, 0, 1, 0, 0, 0, 2, 1, 2, 2, 1, 2, 0, 1, 2, 0, 1, 1, 0, 0, 1, 2, 2, 2, 2, 0, 1, 0, 2, 0, 1, 2, 0, 1, 0, 2, 1, 2, 2, 1, 2, 1, 1, 0, 1, 2, 0, 2, 2, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 2, 0, 2, 0, 0, 1, 0, 0, 2, 1, 1, 0, 0, 1, 1, 2, 2, 2, 1, 2, 0, 2, 1, 1, 2, 1, 0, 1, 1, 0, 2, 0, 2, 0, 1, 0, 0, 1, 2, 1, 0, 1, 1, 0, 0, 2, 1, 2, 1, 0, 0, 2, 0, 0, 2, 2, 1, 0, 2, 1, 1, 0, 2, 0, 2, 2, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 2, 0, 2, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 0, 2, 1, 0, 1, 2, 2, 0, 1, 2, 1, 0, 1, 1, 2, 2, 1, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 2, 1, 0, 2, 2, 2, 1, 0, 1, 0, 2, 2, 1, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 2, 2, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 2, 0, 2, 1, 2, 2, 2, 0, 0, 1, 2, 1, 1, 2, 0, 2, 0, 1, 1, 2, 2, 0, 2, 1, 2, 2, 2, 1, 2, 1, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 2, 0, 2, 1, 2, 0, 0, 0, 0, 2, 0, 1, 2, 1, 1, 2, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 1, 1, 2, 0, 0, 2, 1, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 2, 2, 1, 1, 0, 2, 2, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 1, 2, 1, 1, 2, 2, 0, 0, 0, 2, 0, 0, 0, 0, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 2, 1, 1, 0, 1, 0, 1, 0, 1, 2, 0, 1, 2, 2, 2, 1, 1, 1, 0, 1, 1, 0, 2, 1, 1, 1, 1, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 2, 2, 1, 1, 2, 0, 1, 2, 0, 2, 1, 0, 0, 0, 1, 2, 0, 1, 2, 2, 1, 0, 1, 0, 1, 0, 2, 2, 1, 0, 0, 1, 1, 2, 1, 2, 2, 0, 2, 2, 2, 1, 1, 2, 1, 1, 1, 2, 0, 2, 1, 2, 2, 1, 1, 2, 1, 0, 1, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 2, 0, 0, 1, 0, 1, 0, 2, 1, 2, 2, 0, 2, 2, 0, 1, 1, 1, 0, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 2, 0, 2, 1, 1, 1, 1, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 0, 1, 1, 1, 1, 2, 2, 1, 1, 0, 2, 0, 2, 2, 1, 1, 0, 0, 0, 1, 1, 0, 2, 0, 2, 0, 1, 0, 0, 1, 2, 1, 2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 0, 1, 1, 2, 1, 0, 1, 2, 2, 1, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 2, 0, 2, 2, 0, 2, 2, 2, 0, 1, 0, 0, 1, 2, 1, 1, 0, 0, 2, 1, 1, 1, 2, 2, 0, 2, 2, 2, 1, 2, 0, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 2, 1, 0, 2, 1, 2, 0, 0, 2, 0, 2, 2, 0, 1, 2, 1, 0, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 1, 0, 2, 0, 2, 0, 1, 2, 1, 2, 0, 1, 0, 2, 0, 1, 0, 0, 1, 1, 2, 1, 2, 1, 0, 2, 0, 1, 0, 2, 0, 0, 1, 2, 2, 0, 1, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 0, 0, 0, 0, 2, 2, 1, 2, 2, 1, 1, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 1, 0, 0, 1, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 1, 0, 1, 2, 2, 1, 2, 2, 1, 0, 2, 2, 2, 2, 1, 2, 2, 0, 2, 1, 0, 1, 0, 2, 1, 0, 2, 2, 1, 0, 1, 1, 1, 1, 2, 1, 1, 2, 1, 0, 0, 2, 1, 0, 2, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 1, 2, 2, 2, 1, 2, 0, 1, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 2, 2, 0, 2, 0, 1, 0, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2, 2, 1, 0, 0, 2, 2, 2, 0, 0, 1, 1, 0, 2, 2, 1, 2, 2, 1, 1, 0, 1, 2, 1, 2, 1, 1, 1, 0, 2, 1, 1, 2, 2, 0, 0, 2, 0, 0, 1, 2, 0, 2, 2, 0, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 2, 0, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 0, 2, 2, 1, 2, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 1, 0, 1, 2, 1, 0, 1, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 1, 2, 2, 0, 0, 2, 2, 1, 1, 1, 0, 1, 1, 2, 2, 0, 1, 2, 2, 0, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 1, 0, 2, 2, 2, 1, 0, 2, 1, 1, 2, 1, 1, 0, 0, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 1, 1, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 0, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2, 2, 1, 0, 2, 1, 0, 0, 2, 0, 2, 2, 1, 0, 0, 0, 1, 2, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 0, 2, 0, 1, 2, 1, 2, 1, 1, 0, 2, 1, 1, 2, 0, 2, 0, 2, 2, 2, 2, 1, 0, 2, 1, 1, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 1, 1, 2, 1, 1, 0, 2, 1, 0, 2, 2, 0, 2, 1, 2, 0, 2, 0, 2, 2, 2, 1, 2, 1, 2, 0, 2, 1, 0, 0, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0, 1, 2, 1, 0, 1, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 1, 0, 0, 0, 1, 1, 0, 1, 0, 2, 2, 0, 2, 0, 1, 2, 0, 2, 0, 0, 1, 2, 0, 2, 0, 2, 0, 2, 1, 1, 2, 0, 2, 0, 1, 1, 2, 1, 0, 2, 1, 1, 2, 0, 2, 2, 0, 2, 0, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 0, 2, 1, 2, 1, 2, 1, 0, 1, 1, 2, 1, 2, 0, 2, 0, 0, 1, 0, 1, 2, 0, 0, 0, 1, 2, 1, 1, 0, 2, 2, 2, 0, 2, 2, 0, 0, 0, 0, 2, 1, 2, 2, 2, 1, 2, 0, 0, 1, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 1, 1, 1, 1, 2, 1, 0, 0, 1, 0, 1, 0, 2, 1, 1, 2, 0, 0, 0, 1, 1, 2, 0, 2, 1, 1, 1, 1, 0, 2, 2, 1, 2, 1, 0, 2, 0, 2, 1, 2, 0, 0, 1, 2, 2, 0, 2, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 1, 0, 0, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 0, 2, 1, 1, 0, 1, 2, 1, 2, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 1, 2, 1, 0, 2, 2, 1, 1, 2, 0, 2, 1, 1, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 1, 2, 0, 0, 2, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 0, 2, 2, 0, 2, 0, 0, 0, 2, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 2, 2, 1, 0, 1, 1, 1, 1, 2, 0, 0, 1, 0, 1, 2, 1, 2, 1, 0, 0, 0, 1, 0, 1, 0, 1, 2, 1, 2, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 2, 2, 1, 2, 1, 1, 0, 1, 2, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 2, 1, 0, 0, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 0, 0, 1, 2, 0, 2, 2, 1, 2, 0, 0, 0, 1, 1, 1, 1, 0, 0, 2, 2, 1, 2, 0, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 0, 2, 0, 1, 1, 0, 1, 1, 2, 0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 0, 1, 1, 2, 2, 1, 0, 0, 2, 0, 1, 2, 1, 1, 0, 1, 1, 0, 2, 2, 0, 1, 1, 2, 1, 2, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 2, 0, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 2, 2, 1, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 0, 2, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 2, 0, 0, 0, 2, 2, 0, 2, 2, 0, 2, 1, 1, 2, 1, 1, 0, 2, 0, 2, 0, 0, 0, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 1, 0, 2, 1, 2, 2, 0, 2, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 1, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 2, 0, 0, 1, 1, 2, 1, 0, 0, 1, 0, 0, 1, 0, 0, 2, 0, 2, 0, 1, 0, 2, 1, 1, 0, 0, 2, 2, 0, 1, 1, 2, 0, 2, 1, 2, 2, 0, 2, 2, 1, 2, 2, 1, 0, 0, 2, 0, 2, 2, 2, 1 ] last modified: 2008-10-06
Lb(204,10) = 122 is found by truncation of: Lb(208,10) = 126 DaH Ub(204,10) = 129 is found by considering shortening to: Ub(203,9) = 129 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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