lower bound: | 112 |
upper bound: | 116 |
Construction of a linear code [180,8,112] over GF(3): [1]: [182, 8, 114] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 0, 1, 0, 1, 1, 0, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 2, 1, 2, 0, 2, 0, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 2, 1, 1, 1, 2, 2, 1, 1, 2, 0, 2, 2, 1, 2, 0, 1, 1, 2, 2, 2, 0, 2, 0, 0, 2, 1, 1, 2, 2, 1, 2, 0, 0, 0, 0, 2, 2, 2, 2, 1, 0, 2, 1, 1, 2, 0, 2, 1, 0, 1, 2, 1, 1, 0, 0, 2, 2, 1, 0, 2, 0, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 0, 2, 0, 1, 1, 1, 2, 1, 1, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0, 0, 1, 2, 1, 1, 0, 1, 2, 0, 0, 0, 2, 2, 1, 1, 2, 0, 1, 2, 0 ] [ 0, 1, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 1, 1, 0, 0, 2, 2, 0, 2, 2, 1, 0, 2, 1, 2, 1, 2, 2, 0, 1, 0, 0, 0, 2, 2, 1, 2, 2, 2, 2, 1, 1, 0, 1, 2, 1, 0, 0, 1, 0, 1, 1, 2, 2, 1, 0, 1, 0, 2, 1, 2, 1, 0, 1, 1, 1, 1, 2, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 1, 0, 0, 2, 1, 1, 0, 1, 1, 2, 0, 2, 0, 1, 1, 2, 1, 2, 0, 0, 0, 0, 1, 0, 1, 1, 2, 0, 2, 1, 2, 1, 1, 0, 1, 0, 2, 2, 1, 2, 1, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 2, 0, 1, 1, 2, 2, 1, 2, 1, 0, 0, 1, 0, 2, 1, 2, 1, 2, 2, 0, 1, 1, 0, 1, 1, 2 ] [ 0, 0, 1, 0, 2, 0, 0, 0, 2, 2, 0, 2, 1, 2, 2, 2, 0, 1, 2, 1, 1, 1, 0, 2, 2, 1, 2, 1, 1, 0, 2, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 0, 0, 2, 2, 1, 0, 0, 1, 1, 0, 2, 1, 1, 0, 1, 0, 1, 0, 2, 1, 1, 2, 1, 2, 1, 0, 0, 2, 0, 1, 0, 1, 1, 0, 1, 0, 2, 2, 0, 2, 1, 0, 0, 2, 1, 2, 2, 1, 1, 0, 1, 2, 0, 1, 0, 0, 1, 0, 2, 1, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 0, 2, 1, 1, 0, 2, 0, 1, 2, 2, 2, 0, 0, 1, 2, 1, 2, 0, 1, 1, 2, 2, 2, 2, 2, 0, 2, 1, 2, 2, 0, 2, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 0, 2, 1, 1, 1, 0, 2, 0, 1, 0, 2, 0, 2, 2, 0, 2, 2, 1, 0, 1, 0 ] [ 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 2, 2, 1, 1, 1, 2, 0, 0, 0, 1, 2, 1, 2, 0, 1, 1, 1, 0, 2, 1, 2, 0, 1, 2, 1, 2, 0, 1, 2, 0, 0, 1, 0, 2, 0, 0, 1, 2, 0, 2, 2, 1, 1, 1, 0, 2, 1, 2, 0, 2, 1, 2, 0, 2, 2, 2, 0, 1, 0, 2, 2, 2, 2, 1, 2, 0, 0, 0, 0, 2, 2, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 0, 2, 1, 2, 0, 2, 0, 1, 2, 2, 0, 2, 2, 2, 0, 0, 0, 1, 2, 1, 0, 2, 0, 2, 1, 0, 2, 0, 1, 2, 2, 1, 1, 2, 0, 2, 0, 2, 0, 0, 1, 1, 0, 2, 1, 0, 2, 2, 1, 0, 0, 1, 2, 0, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 2, 0, 2, 0, 0, 2, 0, 0, 0, 2, 2, 1, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 2, 1, 2, 0, 0, 0, 1, 2, 2, 2, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 2, 1, 1, 1, 0, 2, 1, 1, 2, 2, 0, 1, 2, 2, 2, 2, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 0, 0, 0, 2, 0, 1, 2, 2, 1, 2, 2, 0, 1, 0, 1, 2, 2, 0, 0, 1, 0, 0, 1, 2, 2, 0, 0, 2, 2, 1, 1, 2, 2, 0, 1, 2, 2, 2, 2, 0, 2, 1, 2, 0, 1, 2, 2, 1, 1, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0, 1, 1, 0, 1, 1, 0, 0, 2, 1, 0, 1, 2, 0, 2, 2, 0, 1, 1, 0, 2, 0, 2, 2, 0, 1, 0, 1, 2, 1, 2, 0, 2, 0, 1, 0, 1, 1, 1, 0, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 2, 2, 2, 1, 0, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 2, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 2, 1, 0, 1, 2, 0, 2, 2, 2, 1, 2, 1, 0, 1, 1, 1, 2, 0, 0, 2, 1, 1, 2, 0, 1, 0, 0, 1, 2, 2, 2, 0, 2, 1, 1, 0, 2, 0, 2, 2, 2, 2, 0, 1, 2, 0, 1, 2, 1, 2, 0, 0, 2, 2, 1, 1, 2, 0, 2, 1, 2, 1, 1, 2, 0, 2, 0, 2, 2, 2, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 2, 0, 1, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 1, 1, 2, 1, 0, 0, 1, 2, 1, 1, 1, 0, 2, 2, 2, 2, 1, 0, 2, 0, 0, 1, 1, 2, 1, 1, 2, 1, 0, 1, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2, 2, 2, 2, 0, 2, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 1, 2, 0, 0, 0, 0, 2, 2, 1, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 0, 2, 1, 1, 0, 1, 2, 0, 2, 2, 1, 1, 1, 1, 2, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 1, 2, 1, 2, 2, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 0, 2, 2, 1, 0, 2, 0, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 2, 1, 1, 0, 2, 2, 2, 0, 0, 2, 1, 1, 0, 1, 2, 2, 2, 1, 1, 2, 0, 2, 2, 2, 0, 1, 2, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 2, 0, 2, 2, 0, 1, 1, 1, 1, 2, 1, 0, 2, 0, 0, 0, 1, 0, 1, 2, 0, 2, 2, 0, 0, 0, 2, 2, 0, 1, 2, 1, 0, 1, 1, 2, 1, 2, 2, 2, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] [2]: [180, 8, 112] Linear Code over GF(3) Puncturing of [1] at { 181 .. 182 } last modified: 2009-01-13
Lb(180,8) = 111 GO2 Ub(180,8) = 116 is found by considering truncation to: Ub(178,8) = 114 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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