lower bound: | 102 |
upper bound: | 106 |
Construction of a linear code [168,9,102] over GF(3): [1]: [168, 9, 102] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 1, 1, 2, 1, 0, 1, 0, 0, 1, 2, 2, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 1, 2, 0, 1, 1, 0, 1, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 0, 0, 1, 0, 2, 2, 2, 0, 1, 2, 0, 0, 1, 0, 2, 1, 2, 0, 0, 1, 2, 2, 0, 1, 0, 2, 0, 1, 2, 2, 1, 0, 1, 0, 1, 1, 0, 1, 2, 2, 2, 0, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 0, 2, 1, 0, 2, 1, 2, 1, 1, 2, 1, 0, 0, 2, 2, 0, 1, 2, 2, 0, 1, 0, 0, 2, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 0, 0, 0, 1, 0, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 2, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 2, 0, 1, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 1, 2, 2, 2, 2, 0, 2, 2, 2, 0, 0, 0, 1, 2, 1, 0, 2, 0, 0, 1, 2, 2, 1, 2, 1, 1, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 2, 1, 1, 2, 1, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 1, 2, 0, 1, 2, 1, 1, 0, 1, 2, 0, 0, 2, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 0, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 0, 2, 0, 2, 2, 2, 1, 2, 0, 0, 2, 0, 1, 2, 2, 0, 1, 1, 0, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 0, 2, 1, 1, 2, 2, 1, 1, 2, 1, 0, 1, 2, 2, 1, 0, 2, 2, 0, 2, 2, 2, 2, 1, 1, 2, 0, 2, 1, 0, 0, 1, 0, 2, 2, 0, 1, 1, 2, 2, 0, 0, 2, 1, 0, 0, 1, 2, 1, 2, 2, 2, 1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 2, 1, 2, 0, 2, 2, 2, 1, 0, 2, 0, 2, 1, 1, 2, 2, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 1, 0, 2, 0, 0, 2, 0, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 0, 1, 2, 0, 0, 1, 1, 2, 2, 0, 1, 2, 1, 2, 0, 0, 1, 0, 2, 1, 0, 2, 2, 0, 2, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 0, 2, 1, 2, 2, 2, 2, 2, 0, 2, 0, 1, 0, 1, 1, 1, 1, 1, 2, 0, 1, 1, 0, 2, 2, 0, 1, 2, 0, 0, 2, 2, 1, 1, 1, 0, 2, 0, 0, 0, 1, 1, 2, 2, 0, 2, 1, 0, 1, 0, 2, 1, 2, 2, 2, 1, 2, 2, 1, 1, 2, 0, 1, 1, 2, 0, 2, 2, 1, 2, 2, 0, 0, 1, 0, 2, 1, 1, 0, 1, 1, 1, 2, 2, 1, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 1, 1, 2, 1, 2, 0, 0, 0, 1, 1, 0, 2, 1, 2, 2, 0, 2, 2, 0, 2, 2, 0, 1, 2, 0, 2, 0, 1, 1, 2, 0, 2, 2, 1, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 2, 1, 0, 2, 2, 0, 2, 2, 0, 0, 0, 1, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 0, 0, 0, 1, 1, 2, 1, 2, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 2, 1, 2, 0, 0, 2, 2, 2, 1, 1, 1, 0, 0, 2, 0, 0, 1, 2, 2, 2, 1, 0, 2, 0, 0, 0, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 0, 2, 0, 0, 0, 1, 2, 1, 2, 1, 0, 0, 0, 0, 1, 2, 0, 1, 1, 2, 1, 2, 2, 0, 1, 1, 1, 0, 0, 0, 2, 1, 2, 0, 1, 2, 1, 2, 2, 1, 0, 1, 2, 2, 2, 1, 2, 1, 2, 0, 1, 1, 0, 0, 1, 1, 2, 2, 0, 0, 2, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 2, 1, 1, 1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 2, 2, 2, 1, 0, 2, 0, 2, 1, 0, 0, 2, 1, 0, 1, 1, 0, 2, 0, 0, 0, 0, 2, 1, 1, 2, 0, 0, 2, 0, 1, 1, 2, 0, 1, 2, 0, 2, 2, 2, 2, 0, 0, 1, 2, 1, 2, 2, 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 0, 1, 0, 1, 2, 1, 1, 1, 1, 0, 0, 2, 0, 1, 2, 1, 1, 0, 2, 2, 0, 2, 2, 2, 1, 2, 1, 0, 1, 0, 0, 0, 1, 1, 1, 2, 1, 0, 2, 1, 0, 2, 1, 2, 1, 1, 2, 1, 1, 0, 2, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 1, 0, 2, 1, 2, 1, 2, 0, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 1, 1, 1, 0, 2, 2, 2, 0, 1, 1, 0, 2, 1, 1, 0, 2, 0, 2, 2, 1, 1, 1, 2, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 1, 2, 1, 1, 1, 2, 2, 2, 0, 2, 1, 2, 1, 2, 1, 2, 0, 0, 2, 0, 1, 2, 2, 1, 1, 1, 0, 0, 2, 2, 1, 0, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 0, 2, 1, 1, 1, 2, 1, 2, 2, 1, 0, 0, 2, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 0, 0, 1, 2, 2, 2, 2, 0, 0, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 0, 0, 1, 0, 1, 2, 0, 2, 1, 1, 2, 2, 0, 1, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 1, 0, 1, 1, 2, 2, 1, 0, 2, 0, 0, 0, 2, 2, 2, 0, 1, 0, 0, 2, 2, 0, 0, 0, 1, 1, 2, 0, 0, 2, 2, 1, 1, 1, 1, 2, 2, 2, 0, 0, 2, 0, 0, 0, 1, 1, 1, 2, 2, 0, 0, 2, 1, 0, 0, 0, 2, 0, 2, 0, 2, 1, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 2, 2, 0, 2, 0, 0, 1, 1, 2, 2, 2, 2, 0, 1, 2, 0, 1, 2, 1, 2, 0, 0, 1, 1, 2, 2, 0, 0, 2, 1, 1, 2, 0, 0, 0, 0, 1, 1, 2, 2, 0, 1, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 2, 1, 1, 1, 2, 2, 2, 0, 0, 2, 2, 1, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 ] last modified: 2008-11-04
Lb(168,9) = 101 is found by truncation of: Lb(172,9) = 105 MST Ub(168,9) = 106 Da2
MST: T. Maruta, M. Shinohara & M. Takenaka, Constructing linear codes from some orbits of projectivities, to appear in Discr. Math.
Notes
|