lower bound: | 48 |
upper bound: | 52 |
Construction of a linear code [90,12,48] over GF(3): [1]: [90, 12, 48] Linear Code over GF(3) Code found by Grassl and Han via greedy extension Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 2, 2, 0, 0, 1, 2, 1, 0, 2, 2, 2, 1, 2, 2, 0, 2, 2, 2, 1, 0, 2, 1, 1, 1, 2, 2, 0, 0, 0, 2, 0, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 0, 1, 1, 0, 2, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 0, 1, 2, 2, 2, 1, 1, 0, 2, 2, 2, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 0, 1, 1, 1, 0, 0, 1, 2, 1, 2, 1, 1, 1, 1, 2, 0, 1, 0, 2, 1, 1, 0, 1, 0, 2, 0, 2, 2, 2, 2, 0, 1, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 1, 1, 0, 2, 0, 1, 1, 2, 2, 1, 0, 0, 2, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 1, 0, 2, 2, 1, 0, 2, 2, 1, 2, 1, 1, 2, 2, 0, 1, 1, 1, 1, 1, 2, 1, 1, 0, 0, 2, 1, 0, 2, 1, 2, 2, 2, 1, 1, 0, 0, 2, 2, 1, 2, 2, 1, 1, 1, 1, 0, 1, 2, 1, 1, 1, 2, 1, 0, 1, 2, 2, 2, 1, 0, 2, 2, 0, 2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 2, 2, 2, 0, 0, 1, 2, 1, 2, 1, 0, 2, 2, 2, 0, 2, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 2, 1, 2, 2, 0, 2, 2, 2, 0, 1, 1, 2, 0, 1, 1, 0, 1, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 2, 0, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 1, 0, 1, 1, 2, 2, 1, 0, 1, 1, 0, 1, 2, 0, 1, 2, 2, 0, 0, 1, 0, 2, 2, 2, 1, 2, 2, 0, 1, 2, 2, 0, 0, 1, 2, 0, 2, 0, 2, 1, 0, 0, 1, 0, 0, 1, 0, 2, 2, 2, 1, 2, 2, 1, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 1, 1, 0, 1, 2, 1, 1, 1, 2, 2, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 0, 2, 2, 0, 2, 1, 1, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 2, 0, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 0, 0, 0, 2, 0, 2, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 1, 1, 2, 1, 0, 1, 0, 2, 2, 2, 2, 1, 0, 1, 1, 2, 0, 2, 1, 1, 2, 1, 1, 2, 0, 0, 0, 2, 1, 2, 0, 1, 1, 1, 2, 0, 2, 1, 1, 0, 1, 1, 2, 0, 2, 0, 0, 1, 0, 0, 1, 2, 0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 0, 0, 1, 1, 2, 1, 0, 0, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 1, 2, 0, 1, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 1, 1, 0, 2, 0, 0, 0, 1, 2, 2, 2, 0, 0, 1, 0, 0, 2, 2, 1, 2, 2, 0, 0, 2, 0, 1, 2, 0, 2, 1, 2, 2, 1, 0, 0, 2, 0, 0, 1, 1, 1, 2, 0, 1, 2, 0, 0, 0, 0, 2, 1, 1, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 2, 1, 2, 0, 0, 0, 2, 2, 2, 0, 0, 1, 0, 2, 1, 2, 1, 2, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 2, 1, 2, 2, 1, 0, 1, 0, 2, 1, 1, 0, 0, 1, 0, 2, 1, 0, 0, 2, 0, 0, 1, 2, 1, 2, 2, 0, 1, 1, 0, 1, 1, 0, 2, 1, 0, 2, 2, 2, 2, 1, 0, 1, 0, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 1, 1, 0, 2, 1, 1, 2, 1, 1, 0, 2, 1, 2, 2, 2, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 2, 2, 0, 0, 1, 0, 2, 0, 1, 2, 1, 0, 2, 2, 0, 1, 2, 2, 1, 1, 1, 2, 0, 1, 1, 2, 1, 2, 1, 2, 0, 1, 0, 2, 1, 1, 2, 2, 1, 1, 2, 0, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 1, 1, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 2, 1, 1, 2, 1, 1, 1, 2, 0, 1, 0, 1, 2, 2, 1, 1, 0, 2, 1, 1, 0, 0, 1, 2, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 2, 1, 1, 1, 2, 1, 1, 2, 1, 0, 0, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 0, 1, 1, 0, 1, 0, 1, 1, 2, 2, 1, 1, 0, 1, 2, 2, 1, 1, 2, 0, 2, 0, 2, 1, 0, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 1, 2, 0, 2, 0, 2, 2, 0 ] last modified: 2012-01-20
Lb(90,12) = 47 is found by shortening of: Lb(92,14) = 47 XX Ub(90,12) = 52 is found by considering shortening to: Ub(89,11) = 52 BKn
XX:
Notes
|