lower bound: | 60 |
upper bound: | 65 |
Construction of a linear code [108,11,60] over GF(3): [1]: [108, 11, 60] 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, 0, 2, 2, 0, 1, 0, 2, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 0, 2, 2, 1, 0, 2, 1, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 2, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 0, 0, 0, 1, 1, 2, 0, 0, 1, 0, 1, 0, 2, 0, 0, 2, 0, 1, 0, 2, 1, 0, 0, 1, 0, 1, 2, 0, 0, 1, 2, 1, 1, 2, 2, 2, 0, 1, 1, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 0, 1, 2, 0, 2, 2, 1, 2, 0, 1, 0, 1, 0, 1, 0, 2, 0, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 0, 1, 2, 0, 2, 0, 0, 2, 0, 1, 2, 1, 2, 1, 2, 2, 2, 0, 1, 0, 2, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 2, 1, 1, 0, 2, 1, 0, 0, 2, 0, 2, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 2, 1, 2, 1, 2, 0, 1, 1, 1, 2, 2, 1, 1, 1, 0, 2, 1, 0, 2, 2, 1, 0, 1, 2, 0, 0, 2, 1, 0, 2, 1, 2, 0, 2, 1, 1, 0, 1, 1, 1, 2, 1, 0, 1, 1, 0, 0, 0, 2, 0, 2, 2, 0, 1, 2, 2, 2, 0, 1, 2, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1, 2, 2, 1, 2, 0, 1, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 0, 2, 1, 1, 1, 0, 2, 1, 0, 1, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 1, 0, 1, 1, 1, 0, 1, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 2, 0, 2, 0, 0, 1, 1, 2, 0, 1, 0, 2, 2, 0, 2, 2, 1, 1, 0, 0, 0, 0, 0, 2, 1, 1, 2, 0, 0, 1, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 1, 1, 1, 1, 2, 0, 2, 0, 2, 1, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 2, 0, 1, 0, 0, 2, 2, 0, 1, 2, 2, 1, 2, 0, 1, 0, 2, 1, 2, 0, 0, 1, 1, 1, 1, 1, 0, 2, 2, 1, 0, 2, 0, 2, 0, 2, 0, 1, 1, 1, 1, 0, 2, 2, 1, 0, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2, 0, 0, 2, 1, 0, 1, 2, 2, 0, 2, 2, 2, 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 2, 1, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 1, 0, 1, 0, 2, 1, 2, 0, 2, 0, 0, 1, 2, 0, 2, 0, 2, 2, 1, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 2, 0, 1, 1, 0, 2, 1, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2, 1, 0, 0, 2, 0, 0, 2, 1, 2, 2, 2, 2, 2, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 1, 0, 2, 0, 1, 1, 1, 1, 2, 1, 2, 1, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 1, 2, 0, 1, 1, 1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 1, 2, 2, 1, 0, 0, 1, 1, 0, 2, 1, 0, 1, 1, 2, 2, 1, 2, 0, 2, 0, 0, 2, 2, 2, 1, 2, 0, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 2, 0, 0, 1, 0, 2, 0, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 2, 2, 1, 2, 0, 0, 1, 1, 2, 2, 2, 0, 2, 0, 1, 2, 2, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 1, 2, 1, 0, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 0, 2, 1, 2, 2, 0, 0, 0, 2, 0, 1, 1, 2, 1, 2, 2, 0, 2, 2, 2, 0, 0, 1, 2, 1, 1, 2, 2, 2, 2, 0, 0, 0, 2, 1, 2, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 0, 1, 0, 0, 2, 1, 2, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2, 0, 0, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 0, 2, 0, 0, 1, 0, 2, 0, 2, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 2, 2, 0, 0, 2, 1, 2, 2, 1, 1, 1, 0, 1, 0, 2, 1, 2, 2, 0, 2, 2, 2, 1, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 1, 1, 1, 2, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 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, 1, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 0 ] last modified: 2009-06-05
Lb(108,11) = 58 GB4 Ub(108,11) = 65 is found by considering shortening to: Ub(107,10) = 65 LP
LP: Follows from the linear programming bound.
Notes
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