lower bound: | 105 |
upper bound: | 113 |
Construction of a linear code [180,11,105] over GF(3): [1]: [180, 11, 105] 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, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 1, 0, 1, 2, 2, 1, 1, 0, 2, 2, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 2, 2, 0, 1, 0, 2, 1, 0, 0, 2, 2, 0, 1, 2, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 1, 0, 1, 1, 1, 1, 0, 2, 0, 2, 2, 1, 2, 0, 0, 1, 2, 1, 1, 0, 2, 2, 2, 2, 2, 0, 1, 2, 1, 0, 1, 2, 2, 0, 0, 1, 1, 2, 0, 2, 1, 0, 2, 1, 0, 0, 2, 0, 1, 2, 2, 2, 2, 0, 1, 2, 1, 0, 0, 2, 0, 2, 0, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2, 1, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 1, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 1, 2, 2, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 0, 2, 1, 2, 1, 0, 0, 0, 1, 2, 0, 1, 1, 2, 1, 1, 0, 2, 2, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 2, 2, 0, 0, 2, 1, 0, 0, 1, 2, 2, 2, 1, 1, 0, 1, 0, 0, 2, 2, 1, 1, 2, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 2, 2, 0, 2, 1, 0, 2, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 1, 0, 2, 1, 0, 2, 2, 1, 2, 1, 0, 0, 2, 1, 1, 0, 1, 2, 0, 0, 1, 1, 2, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 0, 1, 2, 0, 0, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 0, 2, 0, 2, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 0, 2, 0, 1, 0, 2, 1, 0, 0, 2, 1, 2, 0, 1, 1, 2, 0, 0, 1, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 0, 2, 0, 2, 0, 1, 1, 0, 1, 2, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 2, 1, 0, 2, 0, 1, 0, 1, 1, 0, 2, 1, 2, 0, 1, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 2, 1, 1, 0, 0, 1, 1, 0, 1, 2, 1, 2, 1, 1, 2, 1, 0, 0, 1, 1, 2, 1, 2, 2, 1, 1, 0, 2, 1, 0, 1, 1, 1, 0, 2, 0, 0, 0, 1, 2, 0, 2, 1, 1, 2, 0, 0, 0, 2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 0, 2, 0, 2, 1, 1, 1, 1, 2, 0, 2, 0, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0, 2, 0, 2, 1, 2, 2, 0, 1, 2, 0, 1, 2, 0, 1, 1, 1, 0, 0, 0, 2, 0, 1, 1, 2, 1, 1, 0, 2, 2, 0, 1, 0, 1, 2, 0, 1, 2, 2, 2, 0, 2, 2, 1, 1, 0, 1, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1, 2, 2, 2, 2, 1, 0, 0, 2, 1, 0, 2, 1, 1, 2, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 0, 2, 1, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0, 2, 1, 1, 0, 2, 1, 0, 2, 2, 0, 1, 1, 0, 1, 0, 2, 1, 0, 0, 2, 0, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 1, 1, 2, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 1, 0, 2, 2, 1, 1, 2, 0, 0, 0, 2, 0, 1, 1, 0, 2, 1, 2, 0, 0, 2, 2, 1, 1, 1, 1, 0, 2, 2, 2, 1, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 1, 0, 1, 2, 1, 2, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 2, 2, 1, 1, 0, 1, 0, 1, 0, 2, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 1, 0, 1, 1, 2, 1, 1, 2, 0, 2, 0, 2, 1, 2, 1, 0, 1, 1, 0, 1, 1, 0, 2, 1, 1, 1, 0, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 0, 1, 2, 2, 1, 2, 0, 1, 0, 2, 2, 0, 0, 2, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 2, 0, 1, 0, 0, 2, 2, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 1, 2, 1, 0, 1, 0, 1, 2, 1, 0, 2, 2, 0, 1, 2, 0, 0, 1, 2, 1, 2, 1, 0, 2, 1, 2, 1, 1, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 1, 0, 1, 1, 0, 2, 1, 2, 2, 0, 2, 0, 1, 1, 0, 0, 2, 1, 1, 2, 0, 2, 1, 2, 2, 0, 0, 2, 2, 1, 0, 2, 0, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 0, 1, 2, 0, 2, 1, 2, 0, 0, 0, 2, 2, 0, 1, 2, 1, 1, 0, 1, 0, 2, 0, 0, 2, 0, 1, 1, 1, 0, 1, 0, 2, 0, 1, 1, 0, 2, 0, 1, 0, 2, 0, 1, 1, 0, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 2, 0, 2, 2, 1, 2, 2, 0, 1, 2, 0, 1, 2, 0, 0, 2, 0, 2, 1, 0, 2, 0, 0, 0, 1, 0, 2, 2, 2, 2, 0, 2, 1, 2, 1, 0, 2, 0, 1, 0, 1, 2, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2, 0, 2, 1, 0, 0, 2, 1, 1, 0, 0, 0, 2, 0, 2, 1, 1, 0, 0, 2, 0, 0, 2, 1, 2, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 0, 2, 0, 2, 1, 0, 0, 2, 0, 2, 0, 1, 0, 1, 2, 0, 0, 2, 0, 2, 0, 2, 1, 0, 2, 1, 2, 2, 0, 2, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 1, 0, 1, 2, 2, 0, 1, 2, 1, 1, 0, 2, 1, 1, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 1, 2, 2, 0, 1, 1, 0, 1, 2, 0, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 0, 2, 0, 2, 0, 0, 0, 1, 1, 1, 0, 2, 0, 1, 0, 0, 1, 2, 1, 0, 1, 0, 1, 1, 2, 2, 0, 1, 2, 2, 0, 0, 2, 1, 1, 1, 2, 1, 2, 0, 2, 1, 2, 2, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 2, 0, 1, 0, 2, 0, 0, 1, 2, 1, 1, 2, 2, 2, 2, 0, 0, 0, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 0, 1, 1, 2, 2, 1, 0, 0, 2, 0, 1, 0, 0, 0, 1, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 2, 0, 1, 2, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 0, 1, 0, 0, 1, 1, 1, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 2, 2, 1, 2, 2, 0, 0, 1, 2, 2, 0, 2, 1, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 0, 2, 2, 1, 1, 1, 0, 2, 1, 1, 2, 0, 0, 2, 1, 0, 2, 1, 0, 1, 2, 0, 2, 2, 1, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 1, 1, 2, 2, 0, 1, 1, 2, 0, 0, 2, 0, 0, 1, 1, 2, 0, 2, 2, 0, 2, 2, 0, 1, 1, 0, 0, 2, 0, 1, 2, 1, 0, 1, 0, 2, 2, 1, 2, 1, 0, 0, 0, 2, 1, 2, 2, 2, 0, 2, 1, 1, 0, 2, 2, 2, 0, 0, 1, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 0, 1, 1, 2, 2, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 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, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 0, 0 ] last modified: 2009-08-13
Lb(180,11) = 104 is found by shortening of: Lb(181,12) = 104 is found by truncation of: Lb(182,12) = 105 ARS Ub(180,11) = 113 is found by considering shortening to: Ub(178,9) = 113 is found by considering truncation to: Ub(176,9) = 111 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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