lower bound: | 65 |
upper bound: | 71 |
Construction of a linear code [117,11,65] over GF(3): [1]: [118, 11, 66] 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, 0, 1, 0, 2, 2, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 1, 0, 1, 0, 1, 1, 2, 2, 1, 0, 0, 0, 2, 2, 0, 1, 1, 1, 1, 2, 1, 0, 1, 2, 2, 1, 1, 1, 2, 1, 0, 2, 0, 2, 2, 0, 0, 2, 0, 0, 1, 1, 1, 1, 0, 0, 2, 2, 2, 0, 1, 0, 1, 1, 2, 2, 0, 0, 1, 1, 1, 2, 2, 0, 1, 0, 2, 1, 2, 1, 0, 0, 0, 1, 0, 0, 2, 2, 0, 2, 1, 0, 1, 1, 1, 0, 0, 2, 2, 0, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 2, 0, 2, 1, 0, 0, 1, 0, 2, 1, 2, 1, 0, 0, 1, 2, 2, 1, 1, 2, 0, 0, 0, 2, 1, 2, 1, 2, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 1, 2, 1, 2, 0, 0, 1, 2, 1, 2, 2, 2, 2, 0, 2, 1, 2, 2, 0, 1, 0, 1, 2, 2, 2, 1, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 1, 1, 2, 1, 1, 0, 1, 2, 0, 1, 1, 1, 0, 1, 0, 2, 2, 0, 1, 1, 1, 1, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 2, 1, 2, 0, 0, 2, 2, 1, 0, 0, 1, 2, 2, 0, 2, 0, 2, 1, 0, 0, 1, 1, 2, 0, 1, 0, 1, 1, 1, 1, 2, 0, 0, 1, 0, 2, 1, 2, 2, 2, 1, 1, 0, 0, 2, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 2, 0, 0, 2, 0, 1, 1, 2, 0, 2, 1, 1, 2, 0, 2, 2, 1, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 2, 2, 2, 0, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 0, 0, 0, 0, 2, 2, 2, 0, 2, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 0, 1, 0, 0, 1, 0, 2, 1, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2, 2, 0, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 2, 2, 2, 1, 0, 0, 1, 1, 0, 2, 0, 2, 2, 0, 0, 1, 1, 1, 1, 0, 2, 1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 0, 0, 0, 0, 1, 0, 1, 2, 2, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 2, 0, 2, 0, 0, 2, 1, 1, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 2, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 1, 1, 2, 0, 2, 1, 2, 0, 2, 0, 1, 1, 2, 1, 2, 0, 2, 0, 2, 2, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 2, 2, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 1, 0, 2, 0, 2, 2, 1, 2, 2, 0, 1, 2, 1, 1, 2, 2, 2, 2, 0, 0, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 1, 0, 1, 0, 0, 1, 2, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 2, 1, 0, 1, 2, 0, 1, 1, 0, 2, 1, 1, 1, 2, 0, 2, 2, 0, 0, 1, 2, 1, 0, 0, 2, 1, 2, 0, 2, 1, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 1, 1, 2, 0, 0, 2, 1, 1, 0, 0, 1, 2, 0, 2, 1, 1, 2, 2, 2, 0, 1, 1, 1, 1, 2, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 0, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0, 2, 0, 2, 1, 1, 2, 2, 0, 1, 1, 1, 2, 2, 0, 2, 2, 1, 0, 2, 1, 1, 1, 1, 0, 1, 2, 0, 1, 1, 2, 2, 2, 0, 1, 0, 0, 1, 2, 1, 1, 0, 2, 1, 1, 1, 2, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 2, 2, 2, 0, 0, 1, 0, 2, 0, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 0, 0, 2, 0, 0, 1, 0, 1, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 1, 0, 2, 2, 2, 2, 1, 1, 1, 2, 0, 1, 2, 2, 1, 2, 2, 1, 0, 1, 0, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 1, 0, 2, 1, 2, 2, 2, 2, 1, 1, 2, 0, 2, 2, 1, 2, 2, 1, 2, 0, 2, 1, 0, 1, 2, 2, 1, 1, 0, 1, 0, 1, 0, 1, 2, 0, 1, 2, 2, 1, 1, 2, 0, 1, 0, 2, 0, 2, 2, 1, 0, 1, 1, 0, 0, 2, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 2, 0, 1, 0, 0, 0, 2, 0, 1, 1, 1, 2, 2, 0, 0, 2, 0, 1, 0, 2, 0, 0, 1, 2, 1, 1, 0, 0, 2, 0, 2, 0, 1, 0, 1, 2, 1, 2, 1, 0, 2, 1, 1, 2, 1, 2, 1, 0, 0, 1, 0, 0, 2, 2, 2, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 0, 0, 2, 1, 0, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 0, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 0, 2, 1, 2, 0, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 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, 2, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 2, 1, 2, 2, 0 ] [2]: [117, 11, 65] Linear Code over GF(3) Puncturing of [1] at { 118 } last modified: 2009-06-05
Lb(117,11) = 64 is found by shortening of: Lb(118,12) = 64 is found by truncation of: Lb(120,12) = 66 ARS Ub(117,11) = 71 is found by considering shortening to: Ub(115,9) = 71 LP
LP: Follows from the linear programming bound.
Notes
|