lower bound: | 51 |
upper bound: | 52 |
Construction of a linear code [84,8,51] over GF(3): [1]: [85, 9, 51] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 2, 1, 1, 1, 1, 2, 0, 0, 1, 1, 2, 1, 0, 2, 2, 0, 1, 0, 2, 1, 1, 2, 2, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 1, 1, 2, 1, 0, 0, 2, 2, 0, 1, 2, 1, 1, 1, 2, 0, 1, 0, 0, 2, 2, 1, 1, 1, 0 ] [ 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 1, 2, 1, 1, 1, 2, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 1, 2, 0, 2, 2, 2, 0, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2 ] [ 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 1, 2, 2, 0, 1, 1, 2, 1, 1, 2, 0, 0, 1, 2, 2, 0, 1, 1, 2, 0, 0, 1, 2, 2, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 1, 1, 2, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 0, 1, 2 ] [ 0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 1, 2, 0, 0, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 0, 0, 0, 2, 1, 2, 0, 1, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0, 1, 2, 1, 2, 0, 1, 1, 1, 2, 1, 0, 2, 0, 1, 2, 2, 2, 0, 2, 1, 2, 1, 0, 1, 2, 0, 1, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 2, 2, 1, 0, 1 ] [ 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 2, 2, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 1, 1, 0, 2, 2, 2, 2, 1, 2, 0, 0, 2, 1, 1, 1, 1, 2, 0, 1, 0, 2, 1, 1, 1, 1, 2, 0, 1, 0, 2, 1, 0, 0, 0, 1, 2, 0, 2, 1, 0, 2, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 2, 0, 1, 2, 1, 2, 0, 2, 1, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 2, 1, 0, 1, 0, 2, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 1, 2, 2, 1, 0, 0, 2, 1, 2, 1, 0, 2, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 1, 1, 0, 2, 2, 1, 0, 1, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 1, 2, 2, 0, 1, 1, 2, 0, 1, 2, 0, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 2, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 0, 1, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 0, 1, 2, 1, 2, 0, 0, 2, 1, 1, 0, 2, 2, 1, 0, 0, 2, 1, 2, 1, 0, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 1, 0, 1, 1, 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, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0 ] [2]: [84, 8, 51] Linear Code over GF(3) Shortening of [1] at { 85 } last modified: 2004-04-05
Lb(84,8) = 50 is found by truncation of: Lb(85,8) = 51 MST Ub(84,8) = 52 follows by a one-step Griesmer bound from: Ub(31,7) = 17 is found by considering shortening to: Ub(30,6) = 17 is found by considering truncation to: Ub(28,6) = 15 HHM
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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