lower bound: | 106 |
upper bound: | 110 |
Construction of a linear code [174,9,106] over GF(3): [1]: [176, 9, 108] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 2, 1, 2, 0, 1, 0, 1, 2, 1, 2, 0, 0, 2, 2, 0, 0, 1, 0, 2, 2, 2, 2, 1, 2, 2, 0, 1, 2, 0, 2, 1, 1, 0, 2, 1, 2, 2, 1, 2, 0, 0, 2, 0, 0, 1, 2, 2, 1, 0, 0, 2, 2, 1, 1, 2, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 1, 0, 0, 1, 2, 0, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 0, 1, 1, 2, 1, 0, 2, 0, 1, 0, 1, 1, 0, 1, 1, 2, 2, 2, 2, 0, 0, 1, 2, 2, 1, 0, 1, 0, 0, 1, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 2, 0, 1, 2, 0, 0, 1, 2, 1, 1, 0, 2, 0, 0, 2, 0, 2, 0, 1, 1, 2, 2, 0 ] [ 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 2, 0, 2, 0, 0, 1, 1, 0, 1, 2, 0, 0, 2, 2, 1, 0, 2, 0, 2, 1, 2, 2, 0, 1, 2, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 1, 1, 1, 2, 1, 0, 2, 1, 1, 2, 2, 1, 2, 0, 1, 2, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0, 2, 2, 0, 2, 1, 1, 0, 2, 2, 1, 1, 0, 2, 2, 1, 1, 0, 2, 2, 1, 2, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 0, 2, 2, 1, 1, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2, 0, 1, 1, 2, 1, 2, 2, 1, 1, 0, 1, 2, 2, 1, 0, 2, 2, 2, 2, 1, 0, 1, 1, 1, 0, 1 ] [ 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 2, 2, 1, 0, 1, 2, 2, 1, 2, 0, 2, 0, 0, 1, 1, 0, 0, 2, 2, 1, 0, 1, 0, 1, 2, 1, 0, 2, 1, 1, 0, 0, 0, 2, 1, 1, 1, 0, 0, 2, 1, 1, 2, 1, 0, 1, 2, 2, 0, 0, 1, 2, 1, 2, 0, 1, 1, 0, 1, 1, 0, 2, 2, 2, 2, 2, 2, 0, 0, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 0, 0, 1, 1, 1, 0, 2, 1, 0, 2, 2, 1, 0, 1, 1, 2, 2, 1, 0, 1, 2, 1, 0, 1, 0, 0, 1, 0, 1, 2, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0, 1, 1, 2, 1, 1, 2, 1, 0, 1, 1, 0 ] [ 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 2, 0, 0, 0, 2, 0, 1, 2, 0, 0, 2, 1, 1, 1, 2, 0, 0, 1, 1, 2, 2, 0, 1, 2, 2, 1, 2, 2, 1, 1, 1, 0, 2, 0, 2, 2, 1, 0, 2, 1, 2, 0, 2, 2, 2, 0, 1, 1, 2, 0, 0, 1, 1, 1, 2, 0, 2, 0, 0, 0, 0, 2, 1, 2, 2, 2, 2, 0, 1, 2, 1, 2, 0, 1, 1, 0, 2, 2, 0, 1, 2, 1, 0, 1, 1, 2, 1, 2, 2, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 1, 0, 0, 2, 1, 1, 2, 1, 0, 0, 0, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 0, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 1, 0, 1, 0, 1, 0, 2, 1, 1, 0, 2, 2, 2, 0, 1, 0, 0, 2, 1 ] [ 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 2, 2, 0, 2, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 2, 2, 1, 2, 0, 0, 0, 0, 1, 1, 0, 1, 0, 2, 1, 2, 0, 2, 0, 1, 2, 0, 0, 0, 2, 1, 1, 1, 2, 2, 2, 0, 0, 0, 2, 1, 1, 1, 2, 1, 0, 2, 2, 2, 1, 1, 2, 1, 0, 1, 2, 2, 0, 2, 1, 2, 2, 2, 1, 1, 1, 0, 2, 2, 0, 1, 2, 2, 1, 2, 2, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 1, 1, 2, 0, 2, 0, 2, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 1, 0, 2, 0, 1, 1, 2, 2, 1, 2, 1, 2, 1, 0, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 0, 0, 2, 2, 1, 1, 1, 1, 0, 2, 1, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 1, 1, 0, 2, 0, 2, 0, 2, 2, 1, 2, 2, 1, 2, 2, 0, 1, 0, 2, 0, 2, 0, 1, 1, 1, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 2, 2, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 1, 1, 1, 0, 2, 1, 1, 2, 1, 0, 2, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 1, 1, 1, 0, 1, 0, 1, 1, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 2, 1, 0, 1, 0, 0, 0, 2, 2, 2, 1, 0, 1, 1, 0, 0, 2, 2, 1, 1, 1, 1, 1, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 2, 2, 2, 2, 0, 1, 1, 1, 0, 2, 0, 2, 1, 0, 2, 0, 2, 0, 0, 2, 0, 1, 0, 0, 2, 0, 1, 0, 1, 2, 0, 1, 0, 2, 0, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 2, 2, 1, 1, 0, 0, 0, 0, 1, 0, 2, 1, 2, 2, 2, 1, 2, 2, 0, 2, 1, 2, 2, 1, 0, 1, 2, 1, 2, 0, 1, 2, 1, 1, 2, 1, 0, 2, 1, 2, 1, 2, 0, 1, 2, 1, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 1, 2, 0, 2, 1, 2, 2, 0, 2, 2, 1, 2, 0, 0, 1, 1, 1, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 2, 0, 1, 1, 2, 0, 0, 0, 2, 1, 0, 2, 0, 1, 0, 2, 1, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 2, 1, 0, 2, 0, 2, 1, 0, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 1, 1, 0, 0, 0, 2, 2, 2, 1, 0, 2, 2, 0, 2, 0, 2, 1, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 0, 2, 1 ] [2]: [174, 9, 106] Linear Code over GF(3) Puncturing of [1] at { 175 .. 176 } last modified: 2010-04-28
Lb(174,9) = 105 is found by truncation of: Lb(176,9) = 107 MST Ub(174,9) = 110 is found by considering truncation to: Ub(173,9) = 109 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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