lower bound: | 82 |
upper bound: | 89 |
Construction of a linear code [144,11,82] over GF(3): [1]: [146, 11, 84] 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, 0, 0, 0, 1, 1, 1, 2, 1, 0, 1, 0, 2, 1, 2, 1, 2, 2, 0, 2, 0, 2, 1, 0, 1, 2, 2, 1, 2, 2, 0, 0, 1, 2, 2, 2, 1, 0, 1, 2, 0, 2, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 1, 0, 2, 2, 1, 1, 1, 1, 1, 0, 2, 1, 1, 0, 1, 1, 0, 0, 0, 0, 2, 2, 1, 0, 2, 0, 0, 2, 0, 2, 0, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 2, 0, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 2, 2, 1, 2, 0, 2, 2, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 2, 1, 2, 1, 2, 0, 1, 0, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 2, 1, 1, 1, 1, 1, 0, 2, 0, 2, 2, 1, 1, 0, 1, 0, 0, 2, 0, 1, 0, 0, 1, 0, 2, 2, 1, 2, 2, 1, 1, 2, 2, 0, 2, 0, 0, 1, 0, 0, 2, 2, 0, 0, 2, 1, 2, 2, 1, 0, 2, 2, 1, 1, 1, 0, 0, 0, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 0, 1, 2, 2, 1, 1, 2, 0, 2, 1, 2, 1, 0, 0, 1, 0, 0, 2, 1, 1, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 1, 1, 1, 1, 2, 2, 0, 2, 1, 0, 1, 1, 2, 2, 1, 2, 0, 1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2, 0, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 0, 1, 0, 2, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 0, 2, 2, 2, 0, 1, 2, 2, 0, 2, 1, 0, 0, 1, 2, 2, 1, 0, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 1, 2, 0, 2, 1, 2, 1, 1, 0, 2, 1, 2, 0, 1, 0, 2, 1, 0, 2, 0, 1, 0, 2, 1, 0, 1, 1, 0, 2, 1, 2, 0, 2, 1, 1, 1, 0, 1, 0, 2, 1, 1, 1, 0, 1, 2, 0, 0, 0, 2, 1, 2, 2, 1, 1, 1, 1, 2, 0, 2, 0, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 2, 2, 2, 2, 1, 2, 2, 1, 2, 0, 2, 2, 1, 1, 2, 0, 2, 0, 1, 2, 1, 2, 2, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 2, 2, 2, 2, 2, 0, 2, 1, 0, 2, 0, 1, 0, 1, 2, 2, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 0, 2, 0, 1, 0, 0, 2, 2, 1, 0, 1, 1, 1, 2, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 0, 1, 1, 0, 2, 0, 2, 0, 1, 0, 0, 0, 2, 2, 2, 1, 1, 1, 2, 2, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 1, 1, 2, 0, 0, 2, 2, 2, 1, 1, 0, 0, 2, 0, 2, 2, 1, 0, 1, 0, 1, 1, 2, 0, 0, 0, 0, 2, 0, 0, 1, 1, 0, 2, 2, 0, 1, 2, 1, 1, 0, 1, 2, 1, 2, 1, 2, 0, 1, 1, 2, 1, 0, 0, 0, 2, 2, 2, 2, 1, 1, 2, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 0, 2, 0, 0, 2, 0, 1, 1, 2, 1, 1, 1, 2, 0, 1, 0, 0, 2, 1, 0, 1, 2, 0, 1, 1, 0, 1, 1, 1, 2, 0, 1, 2, 1, 1, 1, 2, 2, 0, 1, 1, 0, 0, 2, 1, 1, 1, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 0, 0, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 1, 2, 2, 0, 2, 1, 2, 1, 0, 0, 0, 1, 2, 2, 0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 2, 1, 1, 1, 1, 0, 1, 2, 2, 2, 1, 0, 0, 2, 2, 1, 1, 0, 0, 2, 0, 0, 2, 0, 1, 1, 0, 1, 1, 1, 2, 0, 1, 1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 0, 2, 1, 0, 2, 1, 0, 1, 1, 0, 0, 2, 0, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 2, 1, 1, 1, 0, 1, 0, 1, 2, 2, 1, 1, 0, 2, 0, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 2, 0, 1, 0, 2, 0, 0, 0, 1, 2, 0, 1, 2, 1, 0, 2, 2, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 0, 0, 1, 2, 0, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 1, 2, 1, 0, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 1, 0, 1, 2, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 2, 2, 2, 0, 0, 1, 1, 2, 2, 0, 1, 2, 1, 1, 0, 0, 2, 1, 1, 0, 1, 0, 1, 0, 0, 2, 1, 0, 2, 2, 2, 0, 0, 1, 2, 0, 2, 0, 1, 0, 0, 0, 1, 2, 1, 2, 2, 1, 0, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 0, 0, 0, 2, 1, 0, 2, 0, 0, 0, 1, 1, 1, 2, 1, 0, 1, 0, 2, 2, 1, 0, 1, 0, 2, 2, 2, 2, 0, 1, 1, 2, 0, 0, 1, 2, 0, 0, 0, 1, 0, 2, 2, 2, 1, 0, 0, 2, 1, 2, 0, 2, 2, 0, 0, 0, 2, 1, 2, 0, 1, 2, 2, 1, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 2, 1, 0, 2, 0, 1, 2, 1, 0, 0, 2, 0, 2, 1, 0, 1, 1, 0, 0, 1, 0, 2, 0, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 0, 0, 1, 2, 0, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2, 2, 1, 0, 1, 2, 1, 0, 2, 2, 1, 1, 1, 0, 1, 2, 1, 0, 1, 1, 2, 1, 1, 2, 2, 2, 2, 0, 1, 1, 2, 0, 2, 1, 2, 1, 2, 1, 0, 2, 0, 0, 2, 0, 2, 2, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 1, 2, 0, 1, 0, 2, 1, 0, 1, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 0, 1, 0, 0, 2, 1, 1, 2, 1, 1, 2, 1, 0, 0, 2, 2, 1, 1, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 1, 2, 1, 1, 0, 1, 1, 0, 1, 2, 0, 2, 1, 2, 1, 2, 2, 1, 2, 2, 0, 2, 0, 0, 2, 0, 0, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 1, 1, 2, 1, 1, 1, 0, 1, 2, 0, 1, 0, 2, 0, 0, 2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 0, 1, 2, 2, 0, 1, 0, 2, 2, 0, 0, 0, 1, 1, 1, 2, 0, 2, 1, 2, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 1, 2, 1, 2, 2, 0, 0, 1, 1, 0, 1, 0, 0, 1, 2, 2, 1, 2, 0, 0, 0, 0, 2, 1, 2, 1, 1, 2, 0, 1, 1, 1, 0, 1, 2, 2, 0, 1, 0, 0, 2, 0, 1, 1, 2, 1, 1, 2, 2, 0, 0, 2, 1, 2, 1, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0 ] [2]: [144, 11, 82] Linear Code over GF(3) Puncturing of [1] at { 145 .. 146 } last modified: 2010-04-28
Lb(144,11) = 81 is found by shortening of: Lb(145,12) = 81 is found by truncation of: Lb(146,12) = 82 ARS Ub(144,11) = 89 is found by considering shortening to: Ub(142,9) = 89 is found by considering truncation to: Ub(141,9) = 88 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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