lower bound: | 63 |
upper bound: | 69 |
Construction of a linear code [114,11,63] over GF(3): [1]: [114, 11, 63] Linear Code over GF(3) Code found by Axel Kohnert and Johannes Zwanzger Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 1, 1, 0, 2, 0, 2, 1, 1, 0, 2, 0, 2, 1, 1, 2, 0, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 1, 1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 0, 2, 1, 2, 1, 1, 1, 0, 1, 2, 0, 2, 2, 2, 1, 0, 1, 1, 2, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 1, 1, 1, 2, 0, 1, 0 ] [ 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 2, 1, 0, 1, 1, 2, 1, 0, 0, 1, 2, 0, 1, 1, 1, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 2, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 0, 0, 0, 1, 0, 2, 1, 1, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0, 1, 2, 1, 0, 1, 2, 2, 1, 1, 1, 1, 2, 2, 0, 2, 2, 1, 0 ] [ 0, 0, 1, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 0, 0, 1, 2, 0, 0, 2, 0, 0, 2, 1, 1, 2, 0, 2, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 2, 0, 1, 1, 0, 1, 2, 2, 0, 1, 0, 2, 2, 0, 2, 2, 1, 1, 2, 1, 2, 1, 0, 1, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 0, 0, 2, 1, 2, 1, 0, 1, 2, 2, 0, 1, 1, 0, 0, 2, 0, 0, 2, 1, 2, 0, 0, 0, 1, 2, 0, 0, 1, 0, 2, 1, 0 ] [ 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1, 2, 0, 2, 0, 0, 2, 1, 2, 2, 1, 0, 1, 1, 2, 0, 0, 0, 0, 2, 0, 1, 1, 0, 0, 1, 1, 0, 2, 1, 1, 2, 2, 1, 0, 2, 2, 0, 0, 0, 2, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 2, 2, 0, 1, 1, 2, 2, 0, 2, 2, 1, 0, 0, 2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 2, 0, 1, 1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 1, 1, 0, 1, 1 ] [ 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 2, 1, 1, 2, 0, 2, 2, 0, 2, 1, 1, 2, 1, 0, 1, 2, 0, 1, 0, 0, 0, 1, 2, 0, 2, 2, 0, 2, 0, 2, 1, 1, 0, 1, 2, 1, 0, 0, 1, 1, 2, 2, 1, 2, 2, 0, 1, 0, 2, 2, 2, 1, 1, 1, 2, 2, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 2, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 2, 1, 2, 0, 0, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 2, 2, 0, 1, 1, 2, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 0, 2, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 1, 1, 1, 2, 0, 0, 0, 1, 0, 1, 2, 0, 1, 2, 2, 0, 1, 1, 0, 1, 1, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 1, 1, 1, 0, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 2, 0, 1, 2, 1, 2, 2, 2, 0, 2, 2, 0, 1, 1, 2, 2, 0, 1, 1, 1, 2, 2, 0, 1, 1, 2, 0, 0, 1, 1, 0, 2, 2, 2, 1, 0, 1, 1, 2, 2, 0, 1, 2, 2, 0, 1, 1, 1, 0, 2, 1, 0, 2, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 1, 2, 2, 2, 1, 0, 0, 0, 1, 2, 0, 2, 0, 2, 1, 1, 1, 2, 2, 0, 1, 2, 0, 2, 0, 0, 0, 2, 1, 2, 0, 0, 1, 0, 1, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 1, 0, 2, 2, 1, 0, 0, 0, 0, 1, 2, 1, 0, 2, 1, 0, 2, 1, 0, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 0, 1, 1, 0, 2, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 0, 1, 1, 2, 2, 2, 1, 0, 0, 0, 1, 2, 0, 2, 2, 1, 2, 2, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 2, 2, 1, 0, 0, 1, 2, 2, 2, 0, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 2, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 1, 1, 0, 1, 2, 1, 1, 2, 0, 0, 1, 1, 2, 2, 1, 0, 1, 2, 0, 1, 2, 2, 1, 0, 2, 1, 0, 1, 1, 2, 0, 1, 1, 0, 1, 1, 1, 2, 2, 1, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 1, 0, 1, 0, 0, 1, 0, 2, 1, 2, 1, 0, 1, 0, 1, 2, 2, 1, 0, 1, 1, 0, 0, 0, 1, 2, 2, 0, 1, 1, 1, 0, 0, 2, 2, 0, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 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, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 1 ] last modified: 2009-06-05
Lb(114,11) = 62 is found by truncation of: Lb(115,11) = 63 Bou Ub(114,11) = 69 is found by considering shortening to: Ub(112,9) = 69 LP
LP: Follows from the linear programming bound.
Notes
|