lower bound: | 82 |
upper bound: | 86 |
Construction of a linear code [138,9,82] over GF(3): [1]: [140, 9, 84] 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, 1, 1, 2, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 2, 2, 1, 1, 0, 0, 0, 2, 2, 2, 1, 0, 2, 1, 0, 1, 1, 2, 0, 2, 2, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 2, 2, 2, 0, 2, 2, 0, 0, 1, 2, 2, 1, 1, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 0, 1, 1, 2, 2, 2, 1, 1, 0, 0, 2, 1, 1, 0, 0, 2, 2, 0, 1, 0, 2, 2, 2, 0, 0, 0, 1, 1, 0, 1, 2, 2, 2, 1, 0, 0, 1, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 2, 0, 1, 1, 0, 0, 0, 1, 2, 2, 1, 1, 2, 2, 2, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 1, 2, 2, 1, 1, 0, 0, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 0, 0, 1, 1, 2, 2, 0, 2, 1, 1, 2, 0, 2, 1, 2, 2, 2, 0, 0, 2, 0, 2, 0, 1, 1, 2, 2, 1, 1, 0, 1, 2, 1, 1, 0, 0, 1, 0, 2, 2, 1, 2, 1, 2, 1, 2, 1, 0, 1, 1, 0, 1, 2, 2, 1, 1, 0, 2, 0, 0, 2, 2, 2, 0, 1, 1, 0, 1, 2, 2, 2, 2, 0, 0, 1, 1, 0, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 0, 1, 0, 0, 2, 2, 1, 1, 2, 0, 0, 0, 2, 2, 2, 0, 1, 2, 0, 1, 2, 1, 0, 0, 1, 2, 0, 2, 2, 0, 2, 0, 2, 0, 0, 1, 2, 1, 2, 1, 2, 0, 0, 0, 2, 1, 0, 2, 1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2, 2, 1, 2, 1, 0, 1, 1, 2, 1, 1, 2, 0, 2, 1, 1, 0, 0, 2, 0, 0, 2, 0, 2, 0, 2, 2, 0, 2, 2, 0, 2, 1, 2, 2, 1, 1, 0, 2, 1, 0, 1, 1, 1, 1, 0, 1, 2, 0, 1, 2, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0, 1, 0, 2, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 1, 1, 2, 1, 0, 0, 0, 0, 2, 1, 2, 1, 0, 2, 2, 2, 2, 1, 1, 1, 0, 2, 0, 1, 0, 0, 2, 2, 0, 1, 0, 0, 1, 1, 2, 0, 1, 1, 2, 1, 0, 0, 2, 2, 1, 1, 2, 1, 2, 2, 0, 2, 1, 1, 1, 1, 1, 0, 0, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 0, 0, 2, 1, 1, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 2, 2, 2, 2, 1, 1, 0, 2, 2, 2, 1, 2, 2, 0, 0, 0, 1, 1, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 2, 0, 0, 2, 1, 2, 2, 2, 0, 2, 0, 1, 2, 2, 1, 1, 0, 0, 2, 2, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 2, 1, 1, 2, 2, 0, 0, 0, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 0, 2, 2, 1, 1, 0, 2, 1, 0, 0, 0, 2, 2, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 0, 0, 0, 1, 0, 0, 2, 1, 0, 2, 2, 1, 2, 0, 0, 2, 2, 0, 1, 2, 1, 2, 2, 0, 2, 1, 2, 0, 2, 0, 1, 1, 2, 1, 2, 2, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 2, 2, 1, 1, 0, 2, 0, 2, 1, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 2, 1, 0, 0, 0, 1, 2, 0, 2, 0, 1, 0, 0, 1, 1, 0, 2, 2, 0, 0, 2, 1, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 1, 0, 0, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 0, 2, 0, 2, 0, 1, 2, 0, 2, 0, 0, 2, 2, 0, 1, 2, 0, 0, 2, 2, 2, 0, 2, 2, 1, 1, 0, 1, 2, 0, 0, 1, 2, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 1, 1, 0, 2, 2, 2, 1, 0, 1, 1, 2, 2, 0, 0, 1, 2, 1, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 1, 1, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 1, 0, 1, 2, 2, 1, 2, 2, 2, 2, 0, 1, 2, 1, 0, 1, 1, 2, 0, 0, 2, 0, 2, 2, 2, 2, 1, 2, 2, 1, 2, 0, 0, 0, 2, 2, 1, 2, 2, 0, 2, 1, 1, 2, 2, 0, 1, 1, 1, 2, 0, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 2, 2, 1, 1, 2, 1, 1, 0, 2, 0, 2, 1, 2, 1, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 2, 2, 0, 0, 0, 1, 1, 2, 2, 0, 0, 0, 2, 0, 1, 2, 2, 1, 0, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 2, 1, 0, 1, 1, 2, 2, 2, 1, 1, 2, 0, 1, 2, 2, 1, 1, 2, 0, 1, 2, 2, 0, 1, 1, 0, 2, 1, 1, 1, 1, 1, 0, 2, 1, 2, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 2, 1, 1, 0, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 0, 1, 2, 1, 2, 2, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 2, 1, 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 0, 0, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 0, 0, 0, 1, 1, 0, 1, 2, 2, 1, 2, 1, 0, 0, 1, 1, 2, 1, 1, 1, 0, 0, 2, 0, 2, 2, 2, 0, 1, 2, 1, 0, 2, 2, 1, 0, 1, 2, 0, 0, 1, 1, 1, 1, 0, 0, 0, 2, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 2, 2, 0, 1, 1, 0, 2, 2, 0, 0, 0, 2, 0, 2, 0, 2, 0, 2, 1, 1, 0, 2, 1, 1, 0, 1, 1, 2, 0, 2, 0, 0, 1, 1, 0, 2, 0, 1, 1, 1, 1, 1, 2, 2, 0, 0, 1, 2, 0, 2, 1, 0, 1, 1, 2, 2, 2, 0, 0, 2, 0, 2, 1 ] [2]: [138, 9, 82] Linear Code over GF(3) Puncturing of [1] at { 139 .. 140 } last modified: 2009-01-13
Lb(138,9) = 81 is found by taking a subcode of: Lb(138,10) = 81 MST Ub(138,9) = 86 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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