lower bound: | 50 |
upper bound: | 51 |
Construction of a linear code [84,9,50] over GF(3): [1]: [84, 9, 50] 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, 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 ] [ 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 ] [ 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 ] [ 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, 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 ] [ 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, 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, 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 ] last modified: 2003-09-25
Lb(84,9) = 49 MST Ub(84,9) = 51 follows by a one-step Griesmer bound from: Ub(32,8) = 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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