lower bound: | 32 |
upper bound: | 35 |
Construction of a linear code [63,11,32] over GF(3): [1]: [64, 11, 33] 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, 1, 0, 1, 1, 2, 1, 1, 2, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 2, 2, 0, 2, 2, 2, 1, 0, 1, 1, 0, 2, 0, 0, 2, 0, 2, 1, 1, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 0, 1, 2, 1, 2, 1, 0, 0, 0, 2, 1, 0, 1, 0, 1, 2, 1, 2, 2, 1, 0, 2, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 2, 2, 0, 0, 1, 2, 0, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 0, 0, 0, 0, 2, 1, 2, 0, 1, 1, 0, 2, 1, 2, 1, 2, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 2, 1, 0, 2, 1, 2, 2, 2, 2, 2, 0, 0, 2, 1, 1, 2, 1, 0, 2, 0, 1, 1, 0, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 1, 2, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 1, 0, 2, 2, 1, 1, 1, 1, 2, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 2, 2, 1, 2, 0, 2, 2, 1, 2, 0, 2, 0, 0, 0, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 2, 1, 0, 2, 0, 1, 2, 1, 1, 0, 1, 0, 2, 1, 1, 2, 2, 1, 0, 2, 2, 2, 1, 0, 2, 0, 2, 2, 1, 0, 2, 1, 0, 1, 2, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 2, 0, 2, 1, 1, 1, 0, 2, 0, 1, 2, 1, 0, 1, 2, 0, 2, 1, 1, 2, 1, 1, 0, 0, 2, 2, 1, 1, 0, 2, 2, 1, 1, 1, 0, 2, 0, 2, 0, 2, 2, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 1, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 1, 0, 1, 1, 1, 2, 1, 0, 2, 2, 0, 0, 0, 2, 0, 0, 2, 1, 2, 0, 1, 1, 1, 2, 0, 2, 1, 2, 2, 0, 0, 2, 1, 2, 1, 0, 2, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 1, 0, 0, 2, 0, 1, 1, 0, 2, 1, 1, 2, 1, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 2, 1, 1, 1, 0, 2, 1, 0, 1, 1, 2, 2, 2, 2, 1, 2, 1, 0, 0, 1, 2, 0, 2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 1, 2, 0, 1, 2, 1, 2, 2, 2, 2, 0, 2, 2, 0, 1, 1, 0, 0, 0, 1, 2, 0, 0, 0, 1, 2, 0, 1, 0, 2, 2, 2, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 2, 1, 0, 2, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 2, 2, 1, 1, 2, 2, 2, 1, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 1, 2, 2, 2, 2, 2, 0, 2, 1, 2, 0, 1, 1, 0, 1, 0, 2, 2, 2, 2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ] [2]: [63, 11, 32] Linear Code over GF(3) Puncturing of [1] at { 64 } last modified: 2009-08-13
Lb(63,11) = 32 is found by lengthening of: Lb(62,11) = 32 DaH Ub(63,11) = 35 is found by considering shortening to: Ub(62,10) = 35 Gur
Gur: Sugi Guritman, Restrictions on the weight distribution of linear codes, Thesis, Techn. Univ. Delft, 2000.
Notes
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