lower bound: | 106 |
upper bound: | 106 |
Construction of a linear code [162,6,106] over GF(3): [1]: [164, 6, 108] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 2, 1, 1, 2, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 2, 0, 2, 0, 2, 2, 0, 0, 1, 2, 1, 2, 2, 1, 1, 2, 0, 1, 0, 1, 0, 1, 0, 2, 1, 1, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2, 1, 2, 1, 0, 0, 2, 1, 1, 2, 1, 1, 0, 0, 2, 2, 2, 1, 1, 0, 1, 2, 0, 1, 2, 0, 0, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0, 1, 2, 2, 0, 2, 1, 2, 0, 0, 2, 2, 1, 1, 1, 2, 2, 0, 0, 1, 2, 0, 1, 2, 2, 1, 1, 0, 1, 0, 2, 2, 1, 2, 1, 0, 1, 0, 2, 0, 1, 1, 0, 1, 2, 2, 2, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2 ] [ 0, 1, 1, 0, 1, 1, 2, 2, 0, 1, 1, 0, 1, 1, 2, 0, 0, 1, 1, 2, 0, 0, 1, 2, 0, 0, 0, 1, 1, 0, 1, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 1, 1, 2, 2, 0, 1, 1, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 1, 2, 2, 0, 1, 2, 0, 0, 1, 1, 2, 0, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 0, 0, 0, 1, 2, 0, 0, 1, 0, 1, 1, 2, 2, 1, 2, 0, 1, 1, 1, 2, 0, 0, 1, 1, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 1, 1, 2, 2, 2, 0, 0, 2, 0, 0, 1, 2, 0, 0, 1, 2, 2, 0, 1, 2, 0, 0, 2, 2, 2, 0, 1, 2, 2, 0, 1, 0, 1, 1, 2, 2, 0, 0, 1, 2, 2 ] [ 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] [ 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, 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, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] [ 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, 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, 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 ] [2]: [162, 6, 106] Linear Code over GF(3) Puncturing of [1] at { 163 .. 164 } last modified: 2001-12-17
Lb(162,6) = 106 is found by truncation of: Lb(164,6) = 108 Bo3 Ub(162,6) = 106 is found by considering truncation to: Ub(161,6) = 105 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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