lower bound: | 115 |
upper bound: | 120 |
Construction of a linear code [189,9,115] over GF(3): [1]: [191, 9, 117] 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, 2, 0, 0, 2, 0, 1, 2, 0, 2, 2, 2, 2, 1, 0, 0, 1, 1, 0, 1, 2, 0, 2, 1, 0, 0, 2, 0, 2, 0, 1, 1, 1, 0, 2, 1, 2, 2, 2, 2, 0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 2, 2, 0, 2, 2, 1, 0, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 0, 1, 0, 2, 1, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 2, 1, 0, 2, 2, 0, 2, 0, 2, 2, 1, 0, 0, 1, 2, 1, 1, 1, 2, 2, 1, 2, 2, 0, 2, 0, 1, 1, 2, 1, 2, 2, 1, 2, 0, 2, 0, 0, 1, 1, 0, 2, 1, 1, 2, 1, 0, 2, 2, 1, 0, 1, 2, 0, 0, 2, 0, 1, 1, 2, 2, 1, 1, 1, 1, 0, 2, 2, 2, 0, 1, 1, 2, 2, 2, 0, 2, 2, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 2, 1, 0, 2, 0, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 2, 1, 0, 2, 2, 2, 0, 2, 2, 0, 1, 0, 2, 0, 2, 2, 1, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 2, 1, 1, 2, 1, 0, 2, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 2, 2, 1, 2, 0, 1, 0, 1, 2, 1, 2, 1, 1, 2, 1, 0, 2, 2, 1, 1, 0, 0, 0, 2, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 1, 1, 0, 0, 2, 1, 2, 0, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 1, 2, 0, 0, 2, 0, 2, 0, 2, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 2, 0, 0, 1, 1, 2, 0, 2, 1, 1, 1, 0, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 0, 1, 1, 1, 0, 0, 2, 1, 2, 0, 1, 1, 2, 0, 2, 0, 2, 2, 1, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 2, 2, 1, 0, 1, 2, 0, 1, 2, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0, 1, 0, 2, 1, 0, 1, 0, 0, 0, 0, 0, 2, 2, 2, 0, 2, 2, 0, 2, 1, 0, 1, 2, 2, 1, 0, 2, 2, 1, 1, 0, 1, 1, 2, 1, 0, 0, 1, 0, 0, 2, 0, 2, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 0, 1, 0, 0, 1, 1, 2, 1, 0, 2, 0, 2, 2, 1, 0, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 1, 0, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 0, 0, 2, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 1, 0, 1, 2, 0, 0, 0, 2, 1, 1, 2, 0, 1, 1, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 2, 1, 0, 2, 0, 2, 1, 1, 1, 2, 0, 0, 0, 0, 2, 1, 0, 2, 0, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 0, 0, 2, 0, 0, 2, 2, 1, 0, 0, 1, 1, 2, 0, 0, 0, 1, 0, 2, 2, 0, 1, 1, 1, 2, 0, 0, 0, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 0, 2, 2, 1, 2, 2, 1, 0, 1, 0, 2, 0, 1, 0, 1, 2, 1, 2, 2, 2, 0, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 0, 1, 1, 2, 2, 0, 0, 2, 1, 1, 0, 2, 2, 2, 1, 0, 1, 0, 2, 0, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 2, 2, 1, 2, 1, 1, 0, 1, 1, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 2, 0, 2, 2, 2, 0, 2, 0, 1, 1, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 0, 0, 1, 2, 2, 1, 2, 0, 2, 2, 0, 1, 0, 1, 2, 1, 2, 2, 1, 2, 0, 1, 0, 2, 1, 0, 0, 1, 1, 1, 1, 2, 0, 1, 1, 0, 0, 1, 2, 2, 2, 2, 1, 0, 1, 1, 1, 1, 2, 2, 0, 1, 1, 2, 0, 2, 2, 0, 1, 2, 1, 2, 1, 0, 0, 0, 1, 1, 2, 2, 2, 2, 0, 2, 0, 0, 1, 0, 1, 2, 1, 0, 0, 1, 2, 1, 0, 1, 1, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2, 2, 1, 1, 2, 0, 1, 0, 2, 1, 1, 0, 1, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 0, 1, 2, 2, 1, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1, 1, 1, 1, 2, 2, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 2, 1, 2, 1, 1, 2, 0, 2, 0, 0, 0, 0, 1, 2, 1, 0, 2, 2, 0, 0, 0, 0, 2, 2, 2, 1, 1, 2, 2, 1, 0, 2, 1, 1, 2, 2, 0, 0, 1, 2, 2, 1, 0, 0, 2, 1, 2, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 0, 1, 0, 1, 1, 2, 0, 0, 0, 2, 1, 1, 0, 0, 2, 1, 2, 1, 1, 1, 0, 2, 2, 1, 0, 1, 0, 2, 0, 1, 2, 1, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 0, 2, 1, 0, 1, 2, 0, 1, 2, 1, 1, 2, 0, 2, 1, 2, 1, 2, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 0, 1, 2, 2, 1, 1, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 2, 1, 1, 0, 2, 1, 0, 1, 2, 1, 0, 2, 0, 2, 0, 0, 1, 2, 2, 0, 0, 2, 1, 2, 1, 2, 0, 1, 0, 1, 0, 2, 2, 0, 2, 1, 0, 2, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 1, 2, 2, 1, 2, 2, 1, 0, 0, 1, 2, 2, 2, 0, 1, 1, 1, 2, 1, 1, 0, 1, 1, 0, 2, 0, 1, 0, 0, 1, 2, 0, 1, 2, 2, 1, 2, 0, 1, 0, 1, 2, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 2, 0, 1, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 1, 1, 2, 1, 0, 1, 2, 0, 1, 0, 1, 2, 1, 0, 0, 0, 2, 1, 0, 1, 2, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 2, 0, 1, 0, 2, 1, 2, 1, 0, 1, 2, 2, 2, 0, 2, 2, 2, 1, 1, 2, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 1, 0, 0, 1, 1, 2, 1, 0, 2, 1, 0, 1, 1, 0, 0, 0, 2, 0, 1, 2, 2, 1, 0, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 1, 1, 0, 1, 1, 1, 2, 0, 2, 2, 1, 1, 0, 0, 2, 2, 0, 1, 2, 2, 0, 1, 2, 2, 1, 0, 2, 0, 1, 0, 2, 1, 2, 2, 2, 2, 0, 1, 0, 1, 1, 0, 1, 2, 2, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 2, 2, 2, 0, 0, 2, 1, 2, 0, 2, 1, 1, 1, 2, 2, 1, 2, 1, 0, 1, 2, 2, 1, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 1, 0, 2, 2, 0, 1, 1, 2, 2, 2, 1, 1, 0, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0, 1, 2, 2, 0, 1, 0, 2, 2, 2, 1, 2, 2, 2, 0, 0, 1, 2, 0, 1, 1, 0, 0, 2, 1, 1, 2, 0, 1, 1, 0, 0, 2, 0, 1, 2, 0, 1, 0, 0, 1, 0, 0, 1, 0, 2, 1, 2, 0, 1, 1, 1, 1, 1, 0, 1, 2, 0, 1, 0, 0, 2, 0, 2, 2, 2, 2, 1, 2, 2, 0, 0, 1, 1, 2, 2, 1, 0, 2, 2, 1, 2, 1, 1, 2, 0, 2, 1, 0, 1, 2, 0, 2, 2, 2, 2, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 0, 2, 2, 2, 1, 0, 1, 2, 1, 0, 1, 2, 2, 0, 2, 2, 0, 2, 0, 1, 0, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 2, 1, 0, 1, 2, 2, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 2, 2 ] [2]: [189, 9, 115] Linear Code over GF(3) Puncturing of [1] at { 190 .. 191 } last modified: 2008-12-05
Lb(189,9) = 114 BZ Ub(189,9) = 120 is found by considering truncation to: Ub(188,9) = 119 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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