lower bound: | 125 |
upper bound: | 130 |
Construction of a linear code [204,9,125] over GF(3): [1]: [205, 9, 126] 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, 1, 2, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 2, 1, 0, 2, 1, 1, 1, 1, 2, 0, 1, 1, 0, 2, 1, 1, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 1, 2, 0, 2, 0, 1, 2, 1, 1, 2, 0, 1, 2, 2, 0, 2, 0, 2, 1, 2, 2, 1, 0, 1, 1, 0, 1, 1, 2, 1, 2, 1, 0, 0, 1, 1, 1, 1, 2, 0, 1, 2, 0, 2, 1, 2, 1, 1, 0, 0, 2, 0, 2, 2, 1, 2, 1, 0, 1, 1, 0, 2, 2, 2, 0, 1, 1, 1, 0, 2, 1, 2, 0, 2, 1, 0, 0, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 0, 1, 2, 2, 0, 2, 0, 0, 1, 2, 1, 2, 0, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 0, 1, 0, 2, 2, 1, 1, 0, 0, 2, 0, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 0, 2, 1, 0, 0, 2, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 0, 0, 1, 0, 1, 2, 1, 2, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 1, 1, 0, 1, 0, 2, 2, 2, 0, 2, 1, 1, 2, 2, 0, 0, 2, 1, 2, 1, 2, 2, 1, 0, 0, 1, 2, 0, 1, 2, 1, 2, 0, 1, 2, 2, 1, 0, 2, 1, 1, 2, 1, 1, 0, 2, 0, 0, 2, 1, 2, 1, 0, 2, 1, 1, 0, 2, 1, 1, 2, 0, 0, 1, 1, 0, 2, 1, 1, 2, 2, 1, 1, 0, 2, 1, 2, 2, 1, 2, 0, 0, 2, 1, 0, 1, 2, 2, 1, 0, 1, 2, 2, 1, 1, 1, 1, 0, 0, 0, 2, 2, 1, 2, 0, 0, 1, 2, 2, 1, 2, 1, 0, 2, 0, 2, 2, 1, 1, 0, 2, 1, 1, 2, 1, 2, 0, 2, 1, 0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 2, 2, 2, 2, 2, 0, 2, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 2, 1, 2, 0, 1, 2, 0, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 1, 0, 2, 2, 0, 2, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 2, 1, 0, 2, 2, 2, 2, 2, 2, 1, 1, 0, 0, 1, 2, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 1, 1, 1, 2, 0, 1, 2, 1, 2, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 0, 2, 2, 1, 1, 1, 0, 1, 0, 0, 2, 1, 0, 2, 2, 1, 0, 0, 1, 2, 2, 1, 2, 1, 1, 2, 0, 1, 2, 1, 2, 2, 0, 2, 0, 1, 2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 1, 2, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 1, 2, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 2, 0, 2, 2, 1, 1, 2, 0, 2, 1, 2, 1, 2, 0, 1, 1, 2, 0, 1, 2, 0, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 1, 1, 2, 2, 0, 1, 0, 0, 2, 1, 0, 1, 2, 1, 0, 0, 2, 2, 2, 0, 0, 2, 0, 2, 1, 0, 1, 2, 0, 2, 0, 1, 2, 1, 1, 2, 2, 1, 1, 0, 2, 2, 2, 1, 1, 2, 0, 1, 0, 0, 0, 0, 1, 2, 1, 2, 2, 0, 1, 0, 1, 1, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 2, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 1, 0, 2, 2, 2, 2, 0, 2, 0, 1, 1, 2, 0, 2, 0, 0, 1, 2, 0, 2, 0, 1, 1, 2, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 0, 0, 0, 2, 0, 1, 1, 1, 0, 0, 1, 2, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 2, 0, 0, 2, 1, 2, 1, 2, 0, 0, 2, 1, 1, 2, 1, 1, 2, 2, 2, 0, 0, 2, 2, 0, 2, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 0, 1, 2, 1, 1, 0, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0, 1, 2, 2, 0, 1, 1, 0, 0, 1, 0, 1, 2, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 2, 2, 1, 1, 1, 2, 0, 0, 2, 0, 1, 2, 1, 0, 0, 1, 0, 2, 2, 2, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 0, 0, 2, 2, 2, 2, 1, 2, 0, 0, 2, 1, 2, 2, 2, 2, 0, 2, 2, 1, 0, 2, 1, 2, 0, 0, 1, 1, 2, 1, 1, 1, 2, 0, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 1, 1, 2, 2, 2, 0, 2, 2, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 1, 1, 1, 0, 0, 2, 2, 1, 0, 2, 0, 1, 1, 0, 2, 2, 2, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 1, 2, 0, 0, 0, 0, 2, 1, 1, 1, 1, 0, 2, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 2, 0, 0, 1, 2, 1, 0, 2, 0, 1, 1, 0, 1, 1, 1, 2, 2, 1, 0, 0, 2, 1, 2, 0, 2, 1, 0, 1, 0, 0, 1, 2, 1, 1, 2, 0, 2, 1, 2, 1, 1, 2, 0, 1, 2, 0, 2, 2, 1, 1, 0, 2, 2, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 0, 2, 1, 2, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 1, 1, 2, 1, 0, 2, 1, 2, 2, 2, 0, 2, 1, 0, 2, 2, 2, 1, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 2, 2, 2, 0, 2, 0, 1, 0, 1, 1, 2, 1, 0, 2, 1, 2, 2, 0, 1, 2, 1, 2, 0, 1, 1, 0, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 0, 2, 0, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 0, 1, 2, 1, 0, 1, 0, 2, 1, 1, 0, 2, 2, 1, 1, 2, 1, 0, 0, 0, 1, 2, 2, 0, 2, 1, 1, 1, 1, 2, 0, 1, 2, 1, 0, 1, 2, 1, 1, 2, 0, 0, 2, 1, 1, 2, 2, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 0, 1, 1, 2, 2, 1, 0, 1, 2, 2, 1, 2, 2, 1, 0, 1, 0, 1, 1, 2, 2, 2, 2, 0, 2, 0, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 1, 2, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 1, 1, 0, 2, 2, 0, 2, 1, 0, 2, 1, 2, 1, 1, 2, 0, 0, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 0, 1, 2, 0, 1, 0, 1, 0, 2, 1, 0, 1, 0, 0, 2, 1, 1, 1, 0, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 1, 2, 2, 1, 1, 2, 0, 1, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 2, 2, 2, 0, 2, 0, 1, 2, 0, 1, 0, 0, 2, 2, 0, 2, 1, 2, 0, 2, 1, 0, 2, 1, 0, 2, 2, 2, 1, 1, 2, 2, 2, 1, 0, 1, 1, 0, 2, 2, 1, 2, 0, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 0, 2, 2, 2, 1, 2, 2, 2, 1, 0, 2, 0, 1, 1, 1, 2, 0, 0, 1, 1, 2, 2, 0, 2, 2, 2, 1, 2, 0, 0, 1, 1, 1, 1, 0, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 1, 0, 1, 1, 2, 1, 1, 1, 1, 1, 2, 0, 0, 2, 0, 2, 1, 1, 1, 1, 0, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 0, 2, 0, 2, 1, 1, 1, 2, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 2, 2, 1, 0, 2, 1, 0, 2, 0, 1, 1, 0, 2, 2, 2, 1, 1, 0, 2, 1, 2, 1, 2, 2, 0, 2, 2, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2, 2, 1, 0, 1, 2, 0, 2, 0, 2, 0, 1, 2, 2, 0, 1, 1, 0, 1, 1, 1, 1, 2, 1, 0, 2, 1, 1, 2, 0, 0, 1, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 1, 1, 1, 0, 1, 1, 1, 0, 2, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 0, 2, 2, 2, 0, 1, 2, 0, 2, 2, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0 ] [2]: [204, 9, 125] Linear Code over GF(3) Puncturing of [1] at { 205 } last modified: 2008-11-04
Lb(204,9) = 123 is found by shortening of: Lb(205,10) = 123 is found by truncation of: Lb(208,10) = 126 DaH Ub(204,9) = 130 is found by considering truncation 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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