lower bound: | 50 |
upper bound: | 52 |
Construction of a linear code [87,10,50] over GF(3): [1]: [89, 11, 51] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 0, 1, 0, 1, 1, 1, 2, 0, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 1, 1, 2, 0, 1, 1, 1, 1, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 2, 2, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0, 1, 0, 0, 2, 2, 0, 1, 1, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 2, 2, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0, 1, 0, 2, 1, 2, 1, 1, 0, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 1, 2, 1, 1, 2, 2, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 2, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 0, 1, 0, 0, 0, 2, 1, 1, 1, 2, 0, 0, 0, 1, 2, 1, 2, 2, 1, 2, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 1, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 1, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 0, 1, 0, 0, 1, 1, 2, 2, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 2, 2, 1, 1, 0, 2, 2, 2, 0, 2, 1, 0, 2, 2, 1, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 2, 1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 0, 2, 0, 0, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 0, 1, 0, 2, 1, 2, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 2, 0, 2, 2, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 2, 0, 2, 1, 0, 2, 1, 0, 1, 2, 0, 2, 0, 2, 1, 0, 2, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 2, 2, 2, 0, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 1, 1, 2, 0, 2, 2, 1, 2, 1, 1, 0, 2, 0, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 2, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1 ] [2]: [88, 10, 51] Linear Code over GF(3) Shortening of [1] at { 89 } [3]: [87, 10, 50] Linear Code over GF(3) Puncturing of [2] at { 88 } last modified: 2007-07-30
Lb(87,10) = 49 is found by shortening of: Lb(88,11) = 49 is found by truncation of: Lb(90,11) = 51 MST Ub(87,10) = 52 is found by considering shortening 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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