lower bound: | 104 |
upper bound: | 109 |
Construction of a linear code [174,10,104] over GF(3): [1]: [174, 10, 104] 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, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 2, 2, 2, 0, 1, 2, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 2, 1, 1, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 2, 2, 2, 1, 1, 2, 0, 2, 2, 0, 2, 2, 1, 2, 0, 2, 1, 2, 0, 1, 1, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 2, 1, 1, 1, 0, 2, 1, 0, 2, 0, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 2, 0, 1, 2, 1, 1, 1, 2, 2, 1, 0, 1, 0, 0, 2, 0, 1, 2, 1, 0, 2, 1, 1, 0, 0, 0, 2, 0, 0, 1, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 1, 2, 0, 1, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 0, 2, 2, 0, 1, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 2, 2, 0, 2, 2, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 0, 2, 0, 1, 1, 1, 0, 0, 2, 2, 2, 0, 2, 1, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 2, 2, 1, 0, 2, 0, 0, 1, 2, 1, 2, 0, 2, 0, 2, 2, 1, 0, 2, 1, 0, 0, 1, 0, 2, 2, 2, 0, 1, 0, 2, 2, 1, 1, 1, 2, 2, 0, 0, 1, 0, 1, 2, 2, 1, 2, 1, 1, 2, 2, 0, 2, 0, 1, 2, 2, 0, 0, 0, 0, 2, 2, 0, 1, 0, 1, 0, 2, 2, 1, 1, 2, 2, 2, 0, 2, 0, 0, 2, 1, 0, 0, 2, 0, 2, 2, 2, 2, 1, 1, 0, 1, 2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 2, 1, 0, 2, 0, 1, 1, 2, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 2, 0, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 0, 0, 2, 1, 2, 0, 2, 1, 0, 0, 0, 2, 2, 2, 1, 1, 0, 1, 2, 2, 1, 0, 2, 2, 0, 1, 1, 2, 1, 0, 1, 2, 0, 1, 0, 2, 1, 1, 0, 1, 1, 1, 2, 0, 2, 0, 2, 1, 1, 2, 1, 2, 2, 1, 0, 1, 0, 2, 2, 1, 2, 1, 2, 1, 2, 2, 0, 2, 0, 1, 0, 0, 1, 2, 1, 2, 1, 0, 1, 1, 1, 0, 2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 1, 1, 0, 1, 1, 0, 0, 1, 2, 1, 1, 1, 2, 0, 2, 1, 1, 2, 2, 1, 2, 1, 2, 0, 2, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 2, 1, 2, 0, 0, 2, 2, 0, 1, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2, 1, 2, 1, 2, 1, 0, 2, 0, 0, 1, 1, 1, 2, 2, 2, 1, 1, 1, 0, 1, 2, 0, 2, 2, 1, 1, 1, 1, 2, 1, 0, 2, 2, 1, 1, 2, 2, 0, 1, 0, 2, 0, 1, 0, 0, 2, 2, 0, 2, 2, 1, 0, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 0, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 2, 2, 1, 2, 0, 1, 0, 2, 2, 0, 2, 1, 1, 0, 2, 2, 1, 1, 0, 2, 2, 0, 0, 1, 0, 2, 2, 0, 0, 1, 0, 1, 2, 1, 2, 2, 2, 1, 1, 0, 0, 1, 0, 1, 2, 2, 2, 0, 0, 1, 2, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 0, 2, 2, 2, 1, 1, 1, 1, 2, 0, 1, 1, 1, 0, 2, 0, 0, 2, 2, 0, 1, 2, 2, 0, 0, 1, 2, 1, 0, 1, 2, 1, 2, 2, 0, 1, 0, 0, 0, 2, 1, 1, 2, 0, 0, 1, 1, 2, 2, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 2, 2, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 2, 0, 0, 1, 2, 1, 2, 2, 0, 1, 2, 2, 0, 1, 1, 1, 0, 2, 2, 2, 2, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 2, 2, 1, 2, 0, 2, 1, 0, 1, 2, 1, 2, 0, 1, 2, 0, 1, 1, 0, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 1, 0, 0, 1, 2, 0, 2, 0, 1, 2, 1, 1, 1, 0, 0, 2, 1, 2, 0, 2, 1, 2, 0, 1, 2, 0, 1, 0, 1, 2, 2, 2, 1, 0, 0, 2, 1, 1, 0, 2, 1, 0, 2, 2, 0, 0, 0, 1, 1, 0, 0, 2, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 2, 1, 2, 1, 1, 0, 0, 2, 2, 2, 1, 0, 0, 1, 2, 2, 1, 2, 0, 1, 1, 1, 0, 2, 0, 1, 2, 0, 2, 0, 2, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 0, 2, 1, 0, 0, 2, 1, 2, 2, 0, 2, 0, 0, 1, 1, 1, 0, 2, 0, 0, 0, 0, 2, 0, 1, 1, 2, 1, 0, 1, 2, 1, 1, 2, 1, 0, 1, 0, 1, 2, 1, 1, 0, 1, 1, 0, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 1, 2, 2, 0, 1, 2, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 2, 1, 1, 1, 0, 0, 1, 1, 1, 0, 2, 0, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 1, 1, 2, 1, 2, 0, 2, 0, 2, 0, 2, 1, 2, 1, 2, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 2, 2, 0, 1, 0, 1, 2, 0, 1, 1, 2, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 2, 2, 2, 2, 0, 2, 1, 0, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 0, 0, 2, 2, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 2, 2, 0, 0, 0, 0, 2, 0, 0, 0, 1, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 2, 1, 0, 1, 0, 0, 0, 2, 2, 0, 1, 1, 0, 1, 0, 1, 0, 1, 2, 2, 2, 1, 2, 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 1, 1, 1, 2, 2, 2, 0, 2, 0, 2, 1, 0, 2, 2, 1, 2, 2, 0, 0, 0, 2, 1, 0, 2, 0, 1, 2, 0, 2, 2, 0, 2, 1, 1, 1, 2, 1, 0, 0, 1, 2, 1, 0, 1, 2, 0, 0, 2, 0, 0, 1, 0, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 0, 2, 0, 2, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 2, 2, 0, 2, 2, 0, 1, 1, 0, 2, 0, 0, 0, 1, 1, 2, 2, 2, 1, 1, 0, 1, 0, 0, 2, 1, 0, 0, 1, 2, 0, 1, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 0, 0, 1, 0, 1, 2, 1, 1, 0, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1 ] last modified: 2008-10-21
Lb(174,10) = 102 is found by truncation of: Lb(175,10) = 103 GW2 Ub(174,10) = 109 is found by considering shortening to: Ub(173,9) = 109 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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