lower bound: | 114 |
upper bound: | 118 |
Construction of a linear code [186,9,114] over GF(3): [1]: [186, 9, 114] 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, 1, 1, 0, 0, 2, 1, 0, 2, 0, 0, 2, 0, 1, 1, 1, 0, 1, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 2, 1, 1, 2, 2, 1, 1, 0, 2, 1, 0, 1, 1, 0, 1, 0, 2, 2, 0, 0, 2, 0, 1, 2, 2, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 2, 0, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 0, 2, 1, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 0, 2, 1, 1, 1, 0, 1, 1, 0, 2, 2, 1, 1, 1, 0, 2, 0, 1, 0, 0, 2, 1, 2, 2, 1, 0, 0, 2, 1, 2, 1, 0, 2, 1, 0, 2, 2, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 0, 1, 2, 1, 0, 0, 2, 1, 2, 1, 2, 2, 2, 0, 0, 0, 2, 0, 2, 1, 1, 0, 1, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 2, 2, 1, 2, 1, 2, 0, 2, 1, 0, 0, 0, 1, 2, 0, 1, 1, 1, 2, 2, 2, 1, 0, 1, 2, 0, 2, 0, 2, 0, 1, 2, 0, 0, 1, 1, 1, 2, 1, 2, 0, 2, 2, 2, 0, 0, 2, 2, 0, 1, 0, 0, 1, 2, 2, 2, 1, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 0, 2, 1, 0, 0, 1, 0, 1, 2, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 1, 2, 2, 0, 0, 2, 2, 0, 2, 0, 2, 0, 0, 2, 1, 1, 1, 2, 1, 2, 1, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 1, 2, 1, 0, 0, 2, 2, 1, 2, 2, 1, 2, 2, 2, 0, 2, 0, 2, 1, 1, 0, 0, 2, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 2, 1, 1, 0, 2, 0, 0, 1, 2, 1, 0, 2, 1, 1, 0, 0, 1, 1, 2, 0, 1, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 1, 1, 2, 0, 0, 1, 2, 1, 1, 0, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 2, 2, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 2, 2, 1, 2, 1, 1, 1, 2, 0, 0, 0, 2, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 0, 0, 1, 1, 0, 2, 0, 0, 1, 2, 1, 1, 2, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, 1, 0, 2, 2, 1, 1, 2, 0, 0, 1, 2, 1, 0, 1, 2, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 1, 2, 1, 2, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 1, 2, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 1, 0, 1, 0, 2, 1, 2, 0, 1, 2, 0, 1, 1, 0, 2, 1, 1, 0, 2, 1, 1, 2, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 2, 2, 2, 1, 0, 0, 0, 2, 0, 2, 0, 1, 2, 2, 0, 1, 0, 0, 0, 2, 1, 2, 2, 0, 2, 2, 2, 0, 2, 1, 1, 1, 2, 0, 2, 2, 0, 2, 2, 1, 0, 0, 1, 1, 1, 0, 1, 2, 1, 1, 2, 2, 1, 2, 0, 1, 1, 1, 0, 0, 1, 0, 1, 2, 0, 1, 2, 1, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 0, 2, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 2, 1, 2, 2, 0, 0, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 0, 2, 0, 2, 1, 2, 0, 0, 0, 1, 1, 2, 2, 2, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 2, 2, 2, 0, 2, 1, 0, 0, 1, 1, 1, 0, 0, 2, 2, 1, 2, 2, 2, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 0, 0, 1, 2, 1, 1, 2, 0, 1, 1, 2, 0, 2, 2, 0, 1, 2, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 0, 1, 2, 0, 2, 2, 2, 1, 2, 0, 0, 2, 1, 0, 2, 2, 0, 1, 0, 0, 2, 0, 1, 1, 1, 1, 0, 0, 1, 2, 0, 0, 1, 0, 2, 2, 2, 2, 2, 1, 1, 0, 1, 0, 2, 0, 1, 1, 2, 2, 2, 1, 2, 1, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 1, 1, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 1, 2, 2, 1, 1, 1, 0, 1, 1, 0, 1, 1, 2, 2, 1, 1, 2, 0, 2, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 2, 2, 0, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 2, 1, 1, 1, 2, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 2, 2, 0, 2, 2, 0, 2, 0, 2, 1, 2, 0, 1, 1, 2, 0, 1, 2, 2, 2, 2, 1, 2, 0, 2, 2, 1, 1, 2, 0, 2, 1, 0, 0, 2, 1, 0, 0, 1, 0, 2, 0, 2, 2, 1, 2, 2, 0, 2, 1, 1, 0, 1, 2, 0, 1, 0, 1, 2, 2, 1, 2, 1, 2, 0, 0, 1, 0, 0, 2, 2, 0, 1, 0, 2, 1, 1, 0, 1, 2, 1, 0, 2, 1, 2, 2, 1, 1, 1, 2, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 1, 0, 0, 2, 1, 1, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 0, 2, 1, 2, 2, 0, 2, 0, 1, 1, 0, 2, 2, 0, 2, 1, 2, 2, 1, 0, 0, 1, 2, 2, 0, 2, 1, 0, 1, 1, 1, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 1, 1, 2, 0, 0, 2, 2, 1, 0, 0, 1, 1, 2, 2, 2, 1, 1, 1, 1, 2, 0, 1, 1, 1, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 0, 2, 1, 0, 2, 2, 1, 1, 2, 0, 1, 0, 1, 1, 1, 2, 1, 0, 2, 2, 1, 1, 2, 2, 2, 0, 2, 0, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 0, 2, 1, 1, 2, 0, 2, 0, 0, 0, 0, 2, 1, 2, 0, 1, 0, 0, 2, 2, 2, 1, 2, 0, 2, 0, 2, 2, 2, 1, 0, 2, 2, 0, 2, 2, 0, 1, 1, 2, 1, 2, 0, 2, 1, 2, 1, 2, 1, 1, 1, 2, 1, 0, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0, 2, 2, 2, 1, 0, 2, 2, 1, 2, 2, 1, 0, 1, 0, 0, 2, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 0, 0, 2, 1, 0, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 0, 2, 1, 2, 1, 0, 1, 1, 2, 1, 0, 1, 0, 1, 0, 2, 2, 1, 1, 1, 2, 2, 1, 1, 0, 1, 0, 1, 1, 0, 2, 1, 2, 1, 0, 1, 2, 2, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 2, 0, 0, 0, 2, 2, 0, 1, 0, 0, 0, 2, 0, 2, 1, 2, 1, 0, 1, 1, 2, 0, 1, 1, 2, 2, 0, 2, 0, 0, 2, 1, 0, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 0, 0, 0, 1, 1, 1, 1, 0, 2, 1, 2, 1, 2, 1, 2, 1, 2, 0, 1, 2, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 1, 1, 1, 0, 2, 1, 0, 2, 2, 0, 2, 1, 2, 0, 1, 2, 2, 2, 2, 0, 1, 2, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 0, 1, 0, 0, 1, 0, 2, 2, 1, 1, 0, 0, 1, 1, 0, 2, 2, 0, 1, 2, 0, 0, 1, 2, 0, 2, 1, 0, 1, 2, 0, 2, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 1, 0, 1, 0, 0, 0, 1, 1, 2, 0, 0, 2, 2, 1, 0, 1, 2, 2, 2, 2, 1, 2, 2, 2, 1, 0, 2, 1, 1, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 0, 0, 1, 1, 0, 2, 2, 0, 1, 1, 1, 2, 2, 1, 2, 1, 0, 2, 2, 0, 0, 0, 1, 0, 1, 1, 0, 2, 1, 0, 0, 1, 2, 2, 1, 1, 2, 2, 0, 1, 2, 1, 1, 2, 0, 1, 2, 0, 0, 0, 0, 1, 0, 2, 1, 1, 2, 0, 1, 1, 2, 0, 0, 0, 2, 2, 2, 2, 2, 0, 2, 1, 1, 2, 0, 2, 1, 2, 1 ] last modified: 2010-04-28
Lb(186,9) = 112 is found by truncation of: Lb(187,9) = 113 MST Ub(186,9) = 118 is found by considering truncation to: Ub(183,9) = 115 Gur
MST: T. Maruta, M. Shinohara & M. Takenaka, Constructing linear codes from some orbits of projectivities, to appear in Discr. Math.
Notes
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