lower bound: | 94 |
upper bound: | 98 |
Construction of a linear code [156,9,94] over GF(3): [1]: [158, 9, 96] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 2, 1, 2, 2, 0, 2, 1, 2, 1, 0, 2, 1, 2, 2, 0, 1, 0, 0, 1, 1, 1, 1, 2, 1, 1, 1, 0, 2, 2, 1, 0, 1, 2, 0, 2, 1, 2, 0, 2, 1, 2, 2, 1, 2, 1, 0, 2, 2, 1, 2, 0, 0, 1, 0, 1, 2, 1, 1, 1, 1, 1, 2, 0, 0, 2, 1, 2, 0, 0, 2, 0, 0, 2, 1, 0, 2, 1, 0, 2, 1, 1, 0, 2, 2, 0, 2, 0, 0, 2, 1, 0, 2, 2, 2, 1, 2, 0, 2, 2, 2, 0, 0, 0, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 0, 0, 0, 1, 1, 0, 1, 0, 2, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 2, 1, 0, 1, 1, 2, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 0, 0, 1, 0, 1, 0, 2, 0, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 2, 1, 1, 0, 1, 2, 2, 2, 0, 2, 2, 2, 0, 0, 2, 1, 0, 1, 1, 0, 2, 2, 2, 0, 0, 1, 0, 2, 1, 1, 1, 1, 0, 0, 2, 0, 2, 2, 2, 1, 1, 1, 2, 1, 1, 0, 0, 1, 0, 2, 0, 1, 0, 2, 1, 2, 2, 0, 1, 0, 1, 2, 1, 2, 2, 1, 0, 0, 0, 2, 1, 0, 0, 2, 0, 1, 1, 1, 0, 2, 1, 0, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 0, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 1, 2, 2, 2, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 2, 2, 2, 0, 2, 1, 1, 2, 2, 0, 2, 0, 2, 2, 1, 2, 1, 1, 2, 1, 0, 1, 2, 2, 1, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 2, 1, 2, 0, 0, 2, 0, 1, 0, 2, 2, 1, 0, 2, 0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 2, 2, 1, 0, 2, 1, 1, 2, 1, 2, 0, 0, 1, 0, 0, 0, 2, 2, 0, 1, 1, 2, 0, 1, 0, 0, 1, 2, 0, 1, 2, 2, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 1, 2, 1, 2, 1, 0, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 0, 1, 1, 2, 2, 0, 2, 2, 0, 1, 1, 0, 0, 0, 0, 2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 2, 2, 1, 2, 0, 1, 1, 2, 0, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 0, 1, 2, 2, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 2, 2, 2, 1, 1, 1, 2, 2, 0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 2, 2, 1, 0, 0, 0, 0, 2, 2, 1, 1, 1, 2, 2, 0, 2, 0, 2, 1, 2, 0, 1, 0, 2, 1, 1, 0, 0, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 0, 1, 1, 0, 2, 1, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 1, 0, 2, 1, 2, 0, 0, 2, 1, 2, 1, 0, 2, 1, 2, 2, 0, 0, 2, 2, 2, 1, 1, 2, 1, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 2, 1, 1, 0, 1, 1, 2, 2, 1, 0, 1, 2, 2, 0, 1, 0, 1, 2, 1, 1, 2, 0, 2, 2, 0, 2, 1, 0, 2, 1, 2, 1, 0, 1, 1, 2, 2, 1, 2, 1, 2, 2, 0, 0, 2, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1, 1, 1, 1, 0, 1, 0, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 0, 0, 0, 1, 2, 0, 2, 1, 2, 1, 1, 1, 1, 1, 0, 0, 2, 0, 2, 1, 1, 0, 1, 1, 2, 2, 2, 1, 2, 0, 2, 2, 1, 2, 2, 1, 1, 2, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 0, 1, 2, 0, 1, 2, 2, 1, 2, 1, 1, 0, 2, 2, 1, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 0, 1, 1, 2, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 1, 2, 0, 2, 2, 1, 1, 0, 0, 2, 0, 2, 1, 1, 2, 2, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 0, 2, 0, 0, 0, 2, 2, 1, 1, 2, 2, 2, 1, 0, 1, 0, 1, 2, 1, 1, 2, 0, 2, 1, 1, 2, 2, 2, 0, 2, 1, 0, 1, 0, 2, 1, 2, 1, 1, 2, 1, 2, 2, 0, 2, 2, 0, 2, 2, 1, 2, 0, 1, 2, 2, 1, 0, 1, 0, 2, 1, 1, 1, 0, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 2, 2, 2, 2, 2, 1, 0, 0, 1, 0, 0, 2, 2, 1, 0, 1, 2, 2, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 2, 0, 1, 2, 0, 2, 1, 2, 1, 2, 1, 1, 1, 0, 1, 1, 1, 1, 0, 2, 1, 0, 2, 1, 2, 2, 1, 1, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 1, 2, 0, 1, 1, 0, 1, 2, 1, 1, 2, 1, 1, 1, 0, 0, 1, 1, 1, 2, 2, 0, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 2, 0, 2, 2, 2, 1, 2, 0, 2, 1, 0, 1, 2, 2, 0, 0, 2, 2, 1, 1, 0, 1, 1, 0, 1, 1, 0, 2, 1, 0, 2, 0, 1, 2, 2, 2, 0, 2, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 1, 2, 2, 2, 0, 1, 1, 1, 2, 0, 2, 2, 1, 1, 0, 2, 2, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 1, 2, 0, 1, 2, 2, 1, 0, 0, 2, 2, 1, 1, 2, 1, 1, 1, 0, 2, 0, 1, 0, 1, 0, 2, 2, 1, 2, 0, 0, 2, 1, 1, 2, 2, 0, 2, 0, 0, 1, 2, 2, 1, 0, 0, 1, 1, 1, 1, 1, 2, 0, 2, 0, 1, 2, 0, 1, 0, 2, 2, 2, 1, 0, 1, 1, 0, 2, 1, 1, 0, 1, 0, 2, 1, 2, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 2, 0, 2, 2, 1, 1, 2, 2, 0, 1, 2, 1, 2, 1, 0, 2, 2, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 0, 0, 1, 0, 0, 1, 2, 0, 1, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 1, 2, 2, 2, 1, 0, 2, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 0, 2, 0, 2, 1, 0, 2, 2, 0, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2, 1, 0, 1, 0, 1, 2, 2, 0, 2, 1, 1, 2, 0, 0, 1, 1, 0, 1, 0, 0, 2, 1, 1, 2, 1, 1, 0, 0, 0, 0, 0, 2, 1, 2, 1, 0, 2, 1, 2, 0, 1, 1, 1, 2, 0, 2, 2, 0, 1, 0, 0, 1, 0, 1, 2, 0, 2, 2, 2, 2, 0, 1, 0, 0, 2, 2, 1, 1, 0, 2, 2, 0, 0, 2, 2, 1, 0, 2, 0, 2, 0, 1, 2, 2, 2, 0, 1, 0, 2, 2, 1, 2, 1, 1, 2, 0, 0, 2, 1, 1, 0, 2, 1, 0, 0, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 1 ] [2]: [156, 9, 94] Linear Code over GF(3) Puncturing of [1] at { 157 .. 158 } last modified: 2012-08-21
Lb(156,9) = 93 is found by shortening of: Lb(157,10) = 93 is found by truncation of: Lb(160,10) = 96 DaH Ub(156,9) = 98 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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