lower bound: | 125 |
upper bound: | 128 |
Construction of a linear code [198,8,125] over GF(3): [1]: [199, 8, 126] Linear Code over GF(3) Code found by Axel Kohnert and Johannes Zwanzger Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 2, 0, 1, 1, 0, 0, 2, 2, 1, 0, 2, 1, 0, 1, 0, 0, 2, 2, 2, 0, 1, 2, 1, 1, 1, 0, 2, 0, 0, 2, 2, 2, 1, 0, 2, 0, 0, 1, 2, 2, 1, 2, 1, 1, 2, 0, 1, 2, 0, 0, 1, 1, 1, 2, 1, 2, 0, 0, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 2, 0, 1, 2, 1, 1, 2, 1, 1, 0, 0, 0, 0, 1, 2, 1, 1, 2, 0, 2, 2, 0, 0, 2, 0, 1, 0, 0, 2, 2, 1, 2, 0, 0, 1, 0, 1, 0, 2, 0, 0, 0, 1, 2, 2, 0, 2, 2, 1, 2, 2, 1, 2, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 2, 0, 1, 1, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 2, 2, 2, 2, 1, 0, 1, 0, 1, 0, 2, 0, 0, 2, 1, 1, 0, 1, 0, 1, 2, 2, 0, 0, 1, 1, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 1, 0, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 2, 0, 1, 2, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 0, 2, 1, 0, 1, 0, 2, 2, 1, 1, 2, 0, 2, 0, 1, 0, 2, 2, 1, 1, 2, 0, 2, 1, 0, 1, 1, 1, 1, 2, 2, 1, 0, 2, 0, 2, 0, 2, 2, 1, 1, 2, 2, 1, 2, 0, 0, 2, 1, 1, 2, 0, 1, 0, 2, 2, 1, 2, 0, 0, 1, 0, 2, 2, 1, 2, 0, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 0, 0, 2, 2, 2, 2, 0, 1, 2, 2, 1, 1, 0, 0, 1, 0, 2, 2, 0, 0, 1, 1, 0, 2, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 1, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 2, 1, 0, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 1, 1, 1, 2, 1, 0, 2, 2, 0, 0, 0, 1, 1, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 2, 2, 0, 1, 2, 0, 1, 2, 2, 1, 2, 2, 1, 2, 1, 2, 0, 2, 2, 1, 2, 1, 0, 0, 0, 0, 1, 1, 0, 2, 0, 1, 0, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 0, 1, 2, 2, 2, 1, 1, 2, 0, 1, 1, 0, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 0, 2, 0, 1, 2, 2, 2, 0, 1, 0, 2, 2, 1, 1, 0, 1, 1, 2, 2, 0, 1, 2, 0, 2, 1, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 2, 1, 0, 2, 1, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 2, 2, 1, 1, 0, 1, 2, 0, 2, 0, 0, 2, 0, 1, 1, 0, 2, 1, 2, 0, 1, 2, 1, 2, 1, 0, 2, 1, 1, 1, 2, 0, 2, 1, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 2, 0, 2, 1, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 0, 2, 0, 0, 2, 2, 2, 1, 1, 0, 2, 2, 2, 0, 2, 0, 1, 1, 2, 2, 0, 1, 2, 0, 1, 1, 1, 1, 2, 0, 2, 2, 0, 2, 0, 0, 1, 2, 2, 0, 1, 2, 0, 1, 0, 2, 1, 1, 1, 2, 1, 0, 1, 0, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 0, 0, 2, 2, 1, 1, 2, 0, 2, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1, 2, 2, 1, 2, 2, 0, 1, 2, 0, 0, 1, 1, 2, 2, 0, 0, 2, 2, 0, 1, 2, 1, 0, 2, 2, 2, 1, 0, 2, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 1, 2, 0, 0, 1, 2, 0, 2, 1, 1, 0, 0, 2, 1, 2, 2, 0, 1, 2, 0, 1, 0, 1, 2, 1, 1, 1, 0, 0, 0, 2, 1, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 0, 2, 2, 1, 2, 0, 0, 1, 1, 0, 1, 1, 0, 2, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 1, 2, 2, 1, 0, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 0, 2, 0, 0, 1, 0, 1, 0, 1, 2, 1, 1, 1, 1, 0, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 1, 1, 2, 0, 0, 1, 1, 2, 0, 1, 0, 2, 0, 2, 1, 0, 1, 2, 2, 1, 0, 1, 1, 2, 2, 1, 2, 2, 0, 1, 2, 1, 1, 2, 0, 1, 2, 0, 1, 2, 2, 0, 2, 1, 2, 0, 1, 2, 0, 2, 0, 1, 2, 2, 0, 1, 2, 2, 0, 2, 1, 2, 0, 0, 1, 2, 0, 1, 2, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 1, 2, 2, 1, 2, 1, 0, 0, 2, 0, 0, 2, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 1, 0, 2, 2, 0, 0, 0, 2, 0, 1, 2, 1, 0, 2, 1, 1, 1, 1, 2, 1, 0, 1, 0, 1, 2, 1, 1, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1, 1, 1, 0, 0, 0, 2, 1, 2, 2, 0, 0, 2, 1, 2, 2, 1, 1, 0, 2, 1, 0, 2, 2, 0, 0, 1, 0, 0, 1, 2, 0, 2, 0, 0, 0, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 2, 0, 1, 1, 0, 0, 1, 0, 2, 0, 2, 2, 0, 2, 1, 0, 2, 2, 0, 1, 1, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 2, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 2, 0, 1, 0, 1, 0, 1, 1, 1, 2, 0, 2, 1, 0, 2, 2, 1, 2, 1, 0, 1, 1, 0, 2, 0, 0, 1, 1, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 2, 1, 2, 2, 2, 1, 2, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 1, 0, 2, 0, 1, 1, 0, 2, 0, 1, 2, 0, 2, 2, 2, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 2, 2, 0, 1, 0, 2, 2, 1, 2, 1, 1, 2, 0, 2, 2, 1, 0, 1, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 1, 0, 0, 2, 2, 1, 2, 1, 0, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 2, 2, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 2, 0, 2, 2, 0, 1, 0, 2, 0, 1, 0, 2, 1, 1, 1, 0, 2, 1, 1, 2, 2, 1, 0, 0, 2, 2, 2, 1, 2, 0, 1, 2, 1, 1, 1, 2, 0, 1, 1, 2, 2, 2, 1, 0, 1, 0, 2, 1, 0, 0, 2, 1, 2, 1, 0, 0, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 2, 1, 2, 0, 1, 1, 0, 0, 1, 1, 2, 0, 1, 1, 2, 0, 1, 1, 1, 0, 1, 2, 2, 0, 2, 0, 1, 2, 0, 2, 0, 2, 1, 0, 1, 1, 2, 2, 2, 1, 0, 2, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 0, 0, 1, 2, 1, 1, 2, 0, 2, 2, 1, 0, 0, 2, 2, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 1, 0, 2, 0, 1, 0, 1, 2, 1, 2, 2, 2, 1, 2, 0, 0, 1, 2, 2, 0, 0, 0, 1, 1, 1, 1, 0, 2, 2, 1, 2, 0, 2, 2, 1, 1, 2, 0, 0, 2, 2, 0, 2, 0, 2, 1, 2, 2, 1, 1, 0, 1, 0, 1, 2, 1, 0, 2, 1, 1, 2, 1, 0, 1, 0, 1, 1, 2, 1, 1, 1, 1, 2, 2, 0, 1, 0, 0, 2, 0, 1, 1, 1, 1, 2, 0, 2, 2, 1, 2, 0, 1, 0, 1, 1, 1, 2, 2, 0, 0, 1, 0, 2, 2, 2, 2, 2 ] [2]: [198, 8, 125] Linear Code over GF(3) Puncturing of [1] at { 199 } last modified: 2010-02-16
Lb(198,8) = 124 is found by truncation of: Lb(200,8) = 126 BKW Ub(198,8) = 128 follows by a one-step Griesmer bound from: Ub(69,7) = 42 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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