lower bound: | 28 |
upper bound: | 31 |
Construction of a linear code [57,11,28] over GF(3): [1]: [59, 11, 30] 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, 2, 0, 1, 2, 0, 1, 1, 2, 0, 2, 0, 1, 1, 1, 2, 0, 1, 2, 0, 2, 0, 2, 2, 2, 0, 2, 1, 0, 0, 0, 1, 0, 0, 2, 0, 0, 0, 1, 1, 1, 2, 1, 1, 0, 1, 0, 0, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 2, 2, 2, 0, 1, 2, 2, 2, 0, 0, 2, 2, 1, 2, 0, 1, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 2, 1, 2, 0, 2, 0, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 0, 2, 2, 0, 1, 0, 1, 2, 0, 2, 0, 1, 2, 0, 0, 2, 2, 1, 1, 1, 1, 2, 1, 0, 2, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 2, 1, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 2, 0, 0, 2, 2, 1, 0, 2, 1, 0, 1, 1, 0, 2, 1, 2, 2, 1, 0, 1, 0, 0, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 0, 1, 1, 0, 1, 1, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 2, 2, 1, 0, 0, 2, 2, 2, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 2, 2, 1, 1, 2, 0, 2, 0, 0, 0, 0, 0, 1, 1, 2, 0, 1, 0, 1, 0, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 1, 0, 0, 0, 2, 2, 1, 2, 2, 1, 0, 0, 0, 1, 1, 1, 0, 2, 1, 2, 1, 0, 1, 0, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 0, 2, 2, 2, 1, 2, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 2, 0, 1, 1, 0, 2, 2, 1, 0, 2, 0, 2, 1, 0, 2, 0, 1, 2, 2, 2, 0, 0, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 1, 0, 2, 2, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 2, 1, 2, 0, 1, 0, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2, 0, 2, 0, 1, 2, 1, 1, 0, 1, 0, 1, 0, 0, 1, 2, 0, 1, 0, 0, 0, 1, 0, 1, 2, 1, 1, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 0, 1, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2, 1, 1, 2, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 0, 0, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 0, 2, 0, 2, 1, 2, 0, 0, 1, 0, 2, 2, 2, 1, 1, 1, 1, 2, 2, 1, 0, 2, 1, 0, 0, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 0, 1, 1, 1, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1 ] [2]: [57, 11, 28] Linear Code over GF(3) Puncturing of [1] at { 58 .. 59 } last modified: 2009-06-05
Lb(57,11) = 27 is found by taking a subcode of: Lb(57,12) = 27 is found by lengthening of: Lb(56,12) = 27 ARS Ub(57,11) = 31 is found by considering shortening to: Ub(55,9) = 31 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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