lower bound: | 52 |
upper bound: | 53 |
Construction of a linear code [87,9,52] over GF(3): [1]: [89, 9, 54] Linear Code over GF(3) Code found by Axel Kohnert and Johannes Zwanzger Construction from a stored generator matrix: [ 1, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 2, 1, 0, 2, 1, 2, 0, 0, 2, 0, 2, 1, 2, 0, 0, 2, 1, 1, 0, 0, 0, 2, 0, 1, 1, 0, 2, 2, 2, 0, 2, 1, 1, 1, 1, 0, 0, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 2, 2, 0, 2, 1, 1, 1, 2, 1, 2, 0, 0, 1, 1, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 1, 1, 2, 1, 2, 0, 1, 2, 2, 0, 1, 2, 1, 0, 2, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 0, 2, 0, 0, 2, 0, 2, 2, 1, 1, 0, 1, 1, 0, 2, 1, 1, 2, 0, 1, 1, 1, 2, 1, 0, 2, 1, 2, 2, 2, 1, 0, 0, 2, 0, 2, 1, 0, 0, 0, 2, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 0, 1, 1, 0, 1, 2, 1, 1, 0, 0, 0, 2, 0, 2, 0, 1, 2, 2, 1, 0, 0, 2, 1, 0, 2, 0, 1, 2, 2, 0, 1, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 2, 0, 2, 0, 0, 1, 1, 1, 2, 2, 1, 1, 2, 1, 0, 2, 0, 0, 1, 1, 1, 0, 2, 0, 0, 2, 1, 1, 0, 2, 1, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 1, 2, 1, 2, 1, 0, 1, 2, 1, 2, 1, 2, 2, 2, 1, 0, 0, 1, 2, 0, 1, 1, 0, 1, 2, 0, 2, 1, 2, 2, 2, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 1, 2, 0, 2, 0, 0, 1, 2, 0, 2, 1, 0, 1, 1, 1, 1, 2, 2, 0, 1, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 1, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 2, 0, 2, 1, 0, 0, 1, 2, 0, 2, 2, 0, 2, 2, 2, 1, 1, 2, 0, 2, 0, 0, 1, 2, 2, 1, 1, 0, 0, 2, 0, 1, 0, 1, 2, 1, 0, 1, 1, 0, 0, 0, 2, 0, 1, 0, 2, 0, 1, 1, 2, 2, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 0, 2, 1, 1, 2, 0, 2, 2, 2, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 1, 2, 2, 1, 1, 1, 0, 2, 2, 2, 0, 0, 2, 1, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0, 1, 2, 1, 0, 2, 1, 0, 2, 2, 2, 0, 2, 1, 1, 1, 1, 0, 0, 2, 1, 2, 1, 0, 1, 1, 0, 1, 2, 1, 0, 0, 0, 2, 1, 1, 0, 2, 0, 2, 0, 1, 2, 1, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 2, 2, 1, 2, 0, 0, 1, 1, 0, 1, 1, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1, 2, 2, 2, 1, 0, 1, 2, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 0, 1, 2, 1, 0, 0, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 1, 0, 1, 2, 0, 2, 2, 0, 0, 2, 0, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0 ] [2]: [87, 9, 52] Linear Code over GF(3) Puncturing of [1] at { 88 .. 89 } last modified: 2007-05-14
Lb(87,9) = 51 is found by truncation of: Lb(90,9) = 54 MST Ub(87,9) = 53 is found by considering shortening to: Ub(86,8) = 53 is found by considering truncation to: Ub(85,8) = 52 BKn
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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