lower bound: | 121 |
upper bound: | 126 |
Construction of a linear code [198,9,121] over GF(3): [1]: [200, 9, 123] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 2, 1, 1, 1, 2, 0, 0, 0, 2, 2, 1, 0, 2, 1, 1, 2, 2, 0, 1, 1, 0, 0, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 0, 0, 2, 2, 2, 0, 1, 1, 1, 0, 1, 2, 1, 2, 1, 0, 0, 1, 2, 0, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 0, 1, 0, 2, 1, 0, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 0, 2, 0, 0, 2, 2, 1, 2, 0, 2, 2, 1, 1, 2, 0, 1, 0, 0, 2, 0, 0, 0, 2, 1, 1, 2, 2, 0, 1, 2, 2, 1, 1, 2, 1, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 0, 0, 2, 0, 0, 0, 1, 1, 1, 2, 0, 2, 1, 1, 2, 0, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 1, 0, 1, 0, 2, 1, 1, 0, 0, 0, 0, 1, 1, 2, 1, 2, 0, 1, 2, 1, 2, 1, 0, 0, 1, 0, 2, 2, 1, 2, 2, 1, 2, 0, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 2, 1, 2, 0, 2, 0, 1, 1, 2, 1, 1, 1, 1, 2, 1, 2, 0, 2, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 1, 1, 2, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 0, 1, 2, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 0, 1, 1, 1, 2, 0, 0, 2, 0, 0, 2, 0, 1, 1, 1, 0, 2, 1, 0, 0, 0, 1, 1, 0, 1, 2, 2, 1, 1, 0, 0, 2, 0, 2, 0, 2, 2, 1, 1, 0, 0, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 2, 2, 2, 2, 0, 2, 1, 0, 2, 0, 0, 0, 0, 1, 0, 1, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 1, 1, 1, 2, 0, 2, 2, 0, 1, 0, 2, 0, 0, 0, 2, 1, 1, 1, 2, 0, 1, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 2, 1, 2, 1, 2, 0, 0, 0, 0, 2, 2, 2, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2, 0, 2, 1, 2, 2, 1, 1, 0, 0, 1, 2, 2, 0, 2, 2, 2, 2, 1, 0, 1, 1, 2, 1, 1, 2, 0, 2, 0, 0, 1, 0, 1, 2, 0, 1, 0, 2, 0, 0, 1, 0, 2, 0, 2, 1, 2, 0, 1, 2, 1, 2, 1, 1, 0, 1, 1, 0, 2, 1, 2, 0, 1, 0, 0, 0, 0, 2, 1, 2, 1, 2, 1, 0, 1, 1, 2, 1, 0, 0, 1, 0, 0, 2, 0, 2, 1, 1, 2, 1, 0, 2, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2, 0, 1, 2, 0, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 2, 0, 1, 0, 1, 2, 2, 0, 2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 2, 1, 1, 1, 2, 0, 0, 1, 2, 2, 1, 2, 1, 1, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 2, 0, 1, 0, 1, 1, 2, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 2, 1, 1, 0, 2, 2, 2, 2, 0, 2, 1, 0, 2, 2, 2, 0, 1, 2, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 2, 0, 2, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 1, 1, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 0, 0, 1, 0, 1, 2, 0, 1, 0, 2, 2, 2, 2, 2, 1, 2, 0, 1, 0, 1, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 0, 2, 2, 0, 1, 2, 1, 0, 1, 0, 1, 2, 2, 0, 2, 2, 1, 2, 0, 1, 1, 1, 2, 0, 1, 0, 0, 0, 2, 1, 2, 1, 1, 1, 0, 1, 2, 1, 2, 0, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 2, 1, 0, 2, 2, 0, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 0, 2, 1, 1, 2, 2, 0, 2, 2, 2, 0, 1, 2, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 2, 1, 2, 1, 0, 2, 1, 0, 0, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 0, 0, 0, 1, 1, 2, 0, 2, 2, 2, 0, 2, 0, 2, 2, 1, 2, 0, 1, 0, 1, 0, 2, 2, 1, 2, 1, 2, 2, 0, 1, 1, 0, 0, 2, 0, 1, 0, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 2, 2, 2, 2, 1, 0, 2, 2, 1, 0, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 1, 1, 2, 2, 0, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 0, 2, 0, 1, 2, 0, 0, 1, 2, 0, 2, 2, 1, 0, 2, 1, 1, 0, 1, 1, 1, 1, 2, 0, 2, 1, 1, 0, 2, 2, 1, 1, 0, 1, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 1, 2, 0, 1, 1, 1, 2, 1, 0, 0, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 2, 2, 2, 1, 1, 0, 2, 1, 2, 2, 2, 1, 2, 2, 2, 0, 0, 1, 1, 0, 1, 1, 1, 0, 2, 1, 0, 0, 0, 1, 0, 1, 1, 2, 2, 2, 0, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 1, 0, 2, 0, 2, 2, 1, 1, 2, 0, 0, 0, 2, 2, 1, 2, 0, 2, 0, 1, 2, 2, 0, 1, 2, 1, 2, 2, 0, 1, 0, 1, 1, 2, 0, 0, 0, 0, 2, 1, 1, 0, 0, 0, 2, 2, 2, 1, 0, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 1, 0, 1, 1, 2, 1, 2, 0, 2, 2, 0, 1, 2, 2, 0, 1, 0, 1, 2, 0, 0, 0, 2, 0, 1, 2, 1, 1, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 0, 2, 2, 2, 1, 1, 0, 2, 1, 2, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 2, 1, 1, 1, 1, 2, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 0, 0, 2, 1, 2, 1, 0, 0, 1, 0, 2, 2, 0, 0, 2, 0, 2, 2, 0, 1, 2, 0, 2, 2, 1, 2, 0, 2, 2, 2, 1, 2, 1, 1, 1, 2, 0, 1, 1, 2, 1, 0, 1, 1, 2, 2, 2, 2, 2, 0, 1, 0, 1, 0, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 2, 1, 2, 0, 1, 0, 1, 0, 0, 0, 2, 0, 2, 1, 1, 1, 0, 1, 1, 0, 1, 2, 0, 1, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 1, 2, 0, 0, 1, 0, 2, 1, 0, 0, 0, 2, 2, 2, 2, 2, 1, 1, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 2, 1, 2, 1, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 1, 1, 0, 2, 1, 0, 1, 0, 1, 2, 1, 1, 1, 0, 0, 1, 0, 0, 2, 1, 2, 1, 2, 2, 2, 2, 2, 0, 0, 2, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 1, 1, 0, 0, 2, 1, 2, 1, 2, 0, 1, 0, 0, 2, 1, 0, 0, 1, 0, 2, 1, 1, 0, 2, 0, 2, 1, 2, 2, 2, 1, 1, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 1, 2, 1, 2, 0, 0, 1, 2, 1, 2, 0, 1, 2, 2, 2, 1, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 0, 2, 0, 1, 2, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 2, 1, 0, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 1, 0, 1, 0, 1, 1, 2, 0, 1, 2, 1, 1, 0, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 0, 0, 1, 0, 0, 2, 1, 1, 0, 2, 1, 0, 0, 2, 0, 1, 0, 2, 2, 2, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 0, 1, 2, 1, 0, 1, 2, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 2, 2, 1, 1, 1, 2, 2, 1, 0, 1, 2, 1, 1, 1, 0, 2, 0, 0, 2, 2, 2, 0, 2, 1, 1, 2, 2, 2, 0, 0, 2, 1, 0, 0, 1, 2, 2, 1, 2, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 1, 2, 1, 1, 0, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2, 0, 1, 1, 1, 1, 1, 0, 2, 2, 2, 0, 2, 2, 2 ] [2]: [198, 9, 121] Linear Code over GF(3) Puncturing of [1] at { 199 .. 200 } last modified: 2009-01-27
Lb(198,9) = 120 BZ Ub(198,9) = 126 is found by considering truncation to: Ub(197,9) = 125 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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