lower bound: | 113 |
upper bound: | 119 |
Construction of a linear code [189,10,113] over GF(3): [1]: [190, 10, 114] 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, 2, 0, 1, 1, 2, 2, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 2, 0, 1, 2, 1, 0, 2, 0, 2, 1, 2, 2, 0, 2, 0, 1, 2, 2, 0, 2, 0, 0, 2, 2, 1, 1, 2, 2, 2, 1, 0, 2, 1, 1, 2, 0, 1, 2, 2, 2, 0, 2, 1, 1, 2, 0, 2, 2, 1, 2, 2, 1, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 0, 1, 1, 2, 0, 2, 2, 0, 1, 1, 2, 0, 1, 0, 1, 1, 0, 1, 0, 2, 2, 2, 2, 1, 1, 1, 2, 0, 1, 2, 0, 2, 2, 1, 0, 0, 1, 1, 2, 1, 0, 0, 0, 2, 2, 1, 1, 0, 1, 2, 0, 2, 1, 0, 0, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 0, 2, 2, 1, 1, 1, 0, 0, 2, 0, 0, 2, 2, 1, 0, 1, 1, 2, 1, 0, 2, 0, 0, 0, 0, 2, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 2, 2, 1, 1, 0, 0, 1, 2, 0, 2, 1, 0, 2, 1, 2, 2, 1, 2, 1, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 1, 2, 1, 1, 1, 2, 1, 0, 0, 0, 2, 2, 2, 0, 0, 1, 1, 1, 0, 0, 2, 2, 2, 1, 0, 2, 1, 2, 0, 2, 2, 0, 1, 0, 1, 1, 0, 2, 2, 2, 2, 2, 1, 2, 0, 1, 2, 2, 2, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 0, 2, 0, 1, 1, 2, 0, 0, 2, 1, 0, 1, 1, 1, 1, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 2, 1, 2, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 0, 2, 2, 1, 1, 1, 1, 2, 0, 2, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 1, 1, 2, 0, 1, 0, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 2, 2, 2, 1, 2, 0, 2, 2, 1, 1, 2, 0, 1, 0, 0, 2, 0, 0, 1, 1, 1, 1, 2, 2, 1, 2, 0, 2, 1, 1, 2, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 0, 1, 1, 0, 2, 2, 1, 1, 1, 2, 2, 0, 2, 1, 0, 1, 0, 2, 0, 2, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 1, 0, 0, 0, 0, 2, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 1, 1, 0, 0, 2, 1, 1, 0, 2, 0, 0, 1, 0, 2, 0, 1, 2, 2, 0, 2, 2, 2, 1, 1, 2, 2, 1, 2, 2, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 0, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 0, 1, 0, 0, 1, 2, 2, 2, 0, 2, 0, 2, 2, 0, 1, 1, 2, 0, 2, 2, 1, 0, 0, 1, 0, 2, 1, 0, 1, 2, 0, 1, 2, 1, 1, 2, 1, 2, 2, 0, 2, 2, 0, 1, 2, 1, 1, 2, 0, 1, 2, 2, 1, 1, 2, 0, 0, 0, 0, 1, 2, 2, 2, 2, 1, 0, 2, 2, 0, 0, 0, 2, 0, 1, 1, 2, 1, 2, 0, 0, 2, 1, 1, 0, 0, 1, 0, 2, 0, 1, 2, 0, 1, 0, 0, 1, 0, 0, 1, 2, 2, 1, 0, 1, 1, 2, 0, 2, 0, 0, 1, 1, 2, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 1, 1, 1, 0, 0, 1, 0, 2, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 2, 2, 2, 1, 0, 2, 1, 2, 0, 1, 1, 1, 2, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 2, 1, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 0, 2, 1, 2, 0, 0, 1, 1, 2, 0, 0, 0, 1, 0, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 2, 0, 1, 2, 1, 2, 2, 2, 2, 0, 0, 0, 1, 1, 2, 0, 0, 2, 1, 2, 2, 0, 1, 1, 2, 1, 0, 1, 2, 1, 2, 1, 1, 1, 1, 0, 0, 1, 1, 0, 2, 2, 2, 0, 0, 1, 1, 2, 1, 0, 2, 0, 2, 2, 1, 2, 0, 2, 2, 2, 0, 0, 1, 0, 2, 2, 1, 1, 2, 2, 2, 1, 0, 2, 2, 2, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 2, 2, 2, 1, 1, 0, 0, 2, 0, 1, 2, 1, 2, 0, 2, 0, 2, 1, 1, 0, 1, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 1, 2, 1, 0, 0, 0, 2, 2, 0, 0, 1, 2, 1, 1, 1, 1, 1, 2, 0, 0, 2, 0, 1, 2, 1, 1, 0, 2, 2, 1, 2, 0, 0, 0, 2, 0, 1, 1, 0, 0, 0, 1, 1, 0, 2, 2, 0, 2, 1, 1, 2, 2, 0, 1, 1, 1, 1, 2, 2, 0, 1, 2, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 2, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 1, 2, 1, 1, 2, 2, 1, 2, 0, 1, 1, 2, 0, 1, 1, 2, 2, 1, 0, 2, 0, 0, 2, 0, 1, 0, 2, 1, 2, 1, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 1, 2, 2, 0, 0, 2, 1, 0, 0, 0, 2, 2, 1, 2, 1, 1, 1, 2, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 2, 2, 2, 1, 1, 0, 1, 0, 1, 2, 0, 2, 2, 0, 2, 1, 0, 0, 0, 0, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 2, 0, 0, 2, 0, 0, 1, 1, 2, 1, 2, 1, 1, 2, 1, 0, 1, 2, 2, 2, 1, 2, 2, 1, 0, 0, 1, 2, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 2, 0, 1, 2, 0, 1, 0, 2, 1, 0, 2, 2, 0, 0, 0, 1, 1, 2, 0, 1, 2, 1, 1, 0, 0, 1, 2, 0, 1, 0, 2, 0, 1, 1, 0, 1, 2, 1, 0, 2, 2, 1, 2, 2, 1, 2, 2, 0, 2, 0, 2, 0, 2, 1, 2, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 1, 0, 2, 0, 2, 1, 0, 0, 1, 2, 2, 2, 0, 2, 1, 1, 2, 1, 1, 0, 0, 0, 0, 2, 2, 2, 1, 0, 1, 1, 0, 0, 1, 2, 1, 2, 0, 1, 0, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 0, 2, 1, 1, 0, 1, 1, 2, 0, 2, 0, 2, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0, 1, 0, 0, 2, 2, 2, 2, 1, 2, 0, 1, 0, 1, 2, 1, 2, 2, 2, 0, 1, 2, 1, 1, 2, 0, 1, 1, 1, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 2, 1, 2, 2, 0, 1, 0, 1, 1, 0, 0, 1, 0, 2, 1, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 2, 0, 0, 0, 1, 2, 1, 2, 0, 2, 2, 1, 0, 1, 0, 0, 2, 1, 2, 1, 0, 2, 2, 0, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 1, 2, 0, 1, 1, 1, 2, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 0, 2, 1, 0, 1, 2, 1, 1, 0, 2, 2, 2, 1, 1, 1, 1, 0, 2, 0, 0, 0, 0, 1, 1, 2, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 0, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 0, 2, 0, 1, 1, 2, 2, 1, 0, 0, 2, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2, 2, 0, 0, 2, 2, 0, 2, 1, 2, 2, 2, 2, 0, 1, 2, 1, 2, 2, 2, 0, 0, 1, 1, 0, 2, 1, 0, 0, 0, 2, 2, 1, 2, 1, 2, 1, 1, 2, 0, 2, 1, 1, 2, 0, 1, 0, 1, 2, 2, 0, 0, 2, 2, 2, 2, 2, 1, 0, 2, 1, 2, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 2, 1, 1, 1, 0, 0, 1, 1, 2, 2, 1, 2, 1, 2, 1, 0, 1, 0, 2, 1, 1, 2, 0, 2, 1, 0, 1, 2, 0, 2, 0, 2, 1, 2, 0, 1, 1, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 1, 2, 0, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 0, 1, 0, 2, 2, 2, 1, 1, 1, 0, 1, 1, 2, 2, 0, 0, 0, 2, 2, 1, 2, 1, 1, 1, 0, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 1, 1, 0, 2, 1, 1, 1, 0, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 1, 2, 1, 1, 1, 2, 2, 2, 1, 0, 0, 2, 0, 2, 1, 2, 0, 1, 2, 1, 2, 1, 0, 2, 1, 1, 0, 1, 2, 0, 1, 1, 1, 1, 2, 1, 1, 0, 2, 2, 1, 2, 0, 0, 0, 2, 1, 1, 2, 1, 2, 0, 1, 2, 2, 2, 1, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 2, 1, 2, 0, 1, 2, 0, 2, 1, 2, 1, 0, 2, 1, 2, 2, 0, 2, 0, 1, 2, 2, 1, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 0 ] [2]: [189, 10, 113] Linear Code over GF(3) Puncturing of [1] at { 190 } last modified: 2010-04-28
Lb(189,10) = 111 is found by truncation of: Lb(192,10) = 114 BZ Ub(189,10) = 119 is found by considering shortening 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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