lower bound: | 108 |
upper bound: | 113 |
Construction of a linear code [180,10,108] over GF(3): [1]: [180, 10, 108] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2, 1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 2, 0, 2, 2, 1, 1, 1, 0, 1, 1, 1, 0, 2, 2, 2, 1, 2, 0, 0, 1, 0, 2, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 1, 0, 2, 2, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 1, 1, 1, 1, 2, 2, 2, 1, 0, 2, 1, 2, 1, 0, 0, 1, 1, 1, 1, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0, 2, 1, 0, 2, 1, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 1, 1, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 1, 1, 0, 1, 2, 1, 1, 1, 0, 0, 1, 0, 2, 0, 0, 0, 1, 1, 2, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 0, 1, 2, 0, 0, 2, 0, 2, 1, 2, 0, 1, 2, 2, 2, 1, 2, 0, 1, 0, 2, 1, 1, 1, 2, 2, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 1, 1, 1, 1, 0, 2, 0, 0, 1, 2, 1, 1, 1, 2, 2, 0, 0, 1, 2, 1, 0, 0, 0, 0, 2, 1, 2, 0, 2, 0, 2, 1, 1, 1, 1, 0, 2, 1, 0, 1, 0, 1, 1, 2, 2, 0, 0, 2, 2, 2, 0, 1, 2, 0, 0, 0, 1, 1, 2, 0, 0, 0, 0, 2, 0, 2, 1, 1, 2, 1, 2, 0, 2, 1, 2, 1, 2, 0, 0, 1, 1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 0, 2, 1, 0, 1, 2, 1, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 0, 0, 2, 2, 2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 2, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 1, 2, 2, 2, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 0, 2, 1, 1, 1, 0, 2, 0, 1, 1, 1, 2, 2, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 1, 0, 2, 0, 1, 2, 1, 1, 0, 0, 2, 2, 1, 0, 2, 2, 1, 2, 2, 2, 0, 0, 1, 2, 1, 2, 2, 1, 0, 1, 1, 0, 2, 1, 0, 2, 1, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 2, 1, 0, 2, 1, 1, 1, 1, 0, 0, 1, 2, 0, 2, 2, 1, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 2, 0, 1, 0, 1, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 2, 2, 1, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 1, 2, 0, 0, 1, 2, 2, 2, 1, 2, 0, 1, 2, 1, 2, 1, 1, 0, 2, 2, 0, 1, 2, 1, 2, 1, 0, 2, 1, 0, 1, 1, 0, 1, 0, 1, 2, 0, 1, 2, 0, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 1, 2, 2, 1, 2, 1, 2, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 2, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 1, 1, 0, 1, 2, 1, 2, 0, 2, 0, 1, 2, 2, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 2, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 0, 1, 0, 2, 1, 0, 2, 2, 0, 1, 0, 0, 2, 1, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 2, 1, 1, 1, 0, 0, 2, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 0, 0, 2, 1, 0, 2, 2, 0, 1, 2, 0, 0, 2, 2, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 0, 1, 2, 1, 2, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 2, 1, 1, 1, 0, 0, 0, 1, 0, 1, 2, 2, 2, 2, 0, 1, 2, 2, 0, 2, 2, 1, 2, 1, 2, 0, 2, 1, 1, 1, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 0, 2, 0, 0, 0, 2, 1, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 1, 2, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 2, 2, 1, 0, 0, 0, 1, 2, 2, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 2, 0, 2, 2, 0, 0, 2, 2, 1, 1, 2, 1, 1, 0, 2, 1, 1, 0, 0, 2, 2, 0, 0, 0, 1, 1, 0, 0, 2, 1, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 2, 2, 1, 2, 1, 1, 0, 0, 1, 1, 1, 0, 2, 1, 2, 0, 1, 2, 2, 1, 2, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 2, 2, 0, 2, 2, 2, 2, 0, 1, 0, 0, 0, 1, 1, 1, 0, 2, 1, 2, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 1, 0, 2, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 2, 0, 2, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 0, 1, 1, 2, 0, 0, 1, 1, 2, 0, 2, 1, 1, 0, 0, 1, 1, 0, 2, 2, 2, 0, 2, 1, 0, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 2, 2, 2, 0, 2, 1, 1, 0, 2, 0, 0, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 0, 2, 0, 2, 2, 0, 1, 1, 1, 1, 2, 0, 2, 2, 0, 0, 1, 0, 0, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 1, 2, 2, 2, 2, 1, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 2, 1, 0, 2, 0, 1, 0, 0, 2, 2, 1, 1, 0, 0, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 0, 1, 1, 2, 1, 1, 2, 2, 2, 1, 0, 1, 0, 1, 1, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0, 2, 0, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 1, 1, 2, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 2, 1, 1, 1, 0, 0, 2, 2, 0, 1, 2, 0, 0, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 0, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 1, 1, 1, 2, 1, 2, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 2, 2, 1, 1, 1, 1, 0, 2, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 1, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 0, 0, 2, 0, 0, 2, 1, 1, 1, 0, 0, 0, 2, 0, 0, 1, 2, 0, 2, 0, 1, 1, 2, 1, 1, 2, 0, 2, 0, 1, 0, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 2, 0, 1, 1, 1, 1, 2, 1, 0, 2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 1, 1, 0, 2, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 1, 0, 1, 1, 2, 2, 2, 0, 2, 2, 1, 1, 0, 1, 2, 1, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 0, 2, 1, 2, 0, 2, 2, 2, 1, 0, 0, 0, 2, 1, 1, 1, 1, 1, 1, 2, 1, 0, 1, 2, 2, 0, 2, 2, 2, 0, 1, 2, 2, 0, 2, 2, 1, 0, 1, 0, 1, 1, 2, 1, 1, 0, 0, 2, 2, 2, 0, 2, 2, 1, 1, 0, 1, 2, 2, 2, 1, 2, 0, 2, 0, 0, 1, 1, 1, 2, 2, 0, 1, 1, 2, 0, 0, 0, 2, 2, 1, 1, 1, 2, 1, 0, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 2, 2, 1, 2, 2, 1, 1, 2, 2, 0, 2, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 1, 1, 0, 0, 1, 1, 0, 2, 1, 2, 2, 0, 2, 0, 2, 0, 1, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 1, 2, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 0, 2, 1, 1, 1, 1, 0, 0, 2, 1, 2, 2, 2, 0, 2, 1, 0, 2, 1, 1, 1, 2, 2, 0, 1, 1, 2, 0, 0, 0, 1, 1, 1, 1, 1, 2, 0, 1, 2, 2, 1, 1, 2, 1, 0, 1, 1, 0, 2, 2, 0, 2, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 2, 1, 2, 0, 0, 0, 0 ] last modified: 2009-12-14
Lb(180,10) = 106 is found by truncation of: Lb(182,10) = 108 DaH Ub(180,10) = 113 is found by considering shortening to: Ub(179,9) = 113 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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