lower bound: | 47 |
upper bound: | 49 |
Construction of a linear code [84,11,47] over GF(3): [1]: [85, 11, 48] 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, 0, 0, 2, 0, 2, 0, 0, 2, 1, 0, 1, 1, 2, 1, 2, 2, 0, 1, 2, 2, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 2, 1, 1, 0, 1, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0, 2, 2, 1, 0, 0, 1, 1, 1, 1, 2, 0, 2, 1, 1, 1, 0, 2, 0, 1, 2, 2, 0, 1, 1, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 2, 2, 2, 2, 0, 2, 0, 1, 1, 2, 0, 0, 0, 1, 2, 1, 0, 1, 0, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 0, 2, 1, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 0, 2, 1, 0, 1, 0, 1, 2, 2, 2, 0, 2, 2, 0, 2, 2, 1, 2, 2, 1, 0, 1, 2, 0, 2, 2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 0, 1, 2, 0, 2, 2, 1, 1, 0, 0, 0, 0, 2, 1, 1, 1, 1, 2, 1, 0, 2, 2, 0, 0, 1, 1, 1, 2, 2, 0, 0, 2, 2, 0, 1, 0, 1, 2, 0, 2, 0, 2, 2, 1, 1, 0, 0, 0, 1, 2, 0, 1, 1, 0, 0, 0, 1, 2, 1, 2, 2, 2, 1, 2, 1, 0, 1, 1, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 1, 1, 1, 0, 0, 2, 0, 0, 1, 2, 2, 1, 2, 0, 2, 1, 0, 2, 0, 0, 2, 2, 1, 2, 2, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 0, 0, 2, 0, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 0, 2, 0, 1, 2, 0, 1, 1, 0, 2, 1, 2, 0, 1, 1, 0, 2, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 2, 1, 1, 1, 0, 0, 2, 0, 0, 1, 2, 2, 1, 2, 0, 2, 1, 0, 2, 0, 0, 2, 2, 1, 2, 2, 0, 0, 1, 0, 0, 2, 2, 2, 1, 0, 0, 0, 2, 0, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 0, 2, 0, 1, 2, 0, 1, 1, 0, 2, 1, 2, 2, 2, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 1, 0, 1, 0, 2, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 1, 2, 0, 2, 2, 0, 2, 2, 1, 1, 2, 1, 2, 1, 1, 0, 2, 2, 1, 1, 1, 2, 1, 0, 1, 1, 2, 0, 0, 0, 1, 1, 1, 0, 2, 1, 1, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 1, 1, 0, 1, 0, 2, 0, 0, 1, 2, 1, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 1, 2, 0, 2, 2, 0, 2, 2, 1, 1, 2, 1, 2, 1, 1, 0, 2, 2, 1, 1, 1, 2, 1, 0, 1, 1, 2, 0, 0, 0, 1, 1, 1, 1, 2, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 1, 2, 2, 0, 2, 1, 0, 2, 2, 2, 2, 2, 2, 1, 2, 1, 0, 0, 1, 1, 2, 1, 0, 0, 2, 2, 2, 1, 0, 1, 1, 1, 2, 1, 0, 2, 2, 2, 0, 1, 0, 1, 0, 1, 2, 2, 0, 0, 1, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 0, 2, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 1, 1, 1, 2, 2, 2, 1, 2, 0, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 2, 0, 1, 1, 1, 0, 0, 0, 1, 2, 0, 2, 2, 2, 2, 0, 0, 2, 1, 2, 0, 1, 2, 0, 1, 1, 1, 1, 0, 1, 1, 2, 2, 1, 2, 2, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 1, 2, 1, 0, 2, 2, 2, 1, 0, 1, 2, 1, 0, 1, 1, 1, 0, 2, 0, 2, 1, 0, 0, 0, 0, 2, 2, 0, 2, 0, 2, 1, 2, 1, 2, 2, 0, 0, 2, 0, 2, 0, 2, 0, 2, 2, 0, 1, 0, 0, 0, 1, 1, 2, 2, 0, 0, 2, 2, 1, 1, 1, 0, 2, 2, 0, 1, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 0, 1, 1, 2, 1, 2, 2, 0, 1, 2, 2, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 2, 1, 1, 0, 1, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0, 2, 2, 1, 0, 0, 1, 1, 1, 1, 2, 0, 2, 1, 1, 1, 0, 2, 0, 1, 2, 2, 1, 0, 0, 1, 0, 0 ] [2]: [84, 11, 47] Linear Code over GF(3) Puncturing of [1] at { 85 } last modified: 2005-04-17
Lb(84,11) = 46 is found by truncation of: Lb(86,11) = 48 MST Ub(84,11) = 49 is found by considering truncation to: Ub(83,11) = 48 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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