lower bound: | 35 |
upper bound: | 39 |
Construction of a linear code [55,8,35] over GF(5): [1]: [55, 8, 35] Linear Code over GF(5) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 4, 0, 0, 3, 3, 2, 0, 4, 2, 2, 2, 1, 1, 1, 2, 0, 0, 1, 0, 3, 1, 4, 0, 4, 4, 4, 3, 3, 1, 4, 3, 3, 1, 0, 3, 0, 1, 3, 3, 4, 2, 2, 3, 4, 4, 2, 0, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 2, 3, 0, 3, 4, 4, 4, 0, 4, 0, 3, 3, 1, 0, 3, 3, 3, 2, 3, 0, 4, 4, 1, 2, 2, 0, 4, 1, 2, 2, 4, 2, 3, 1, 1, 2, 2, 2, 3, 1, 0, 1, 4, 1, 2, 3, 0, 3 ] [ 0, 0, 1, 0, 0, 0, 0, 3, 2, 0, 4, 4, 0, 2, 4, 1, 2, 1, 0, 0, 4, 0, 2, 2, 2, 2, 2, 1, 0, 2, 4, 1, 0, 2, 4, 2, 1, 4, 1, 2, 4, 2, 4, 4, 4, 1, 0, 1, 0, 2, 1, 4, 2, 1, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 4, 0, 4, 3, 3, 0, 2, 0, 3, 0, 1, 4, 2, 2, 4, 4, 4, 3, 3, 1, 4, 2, 3, 1, 2, 0, 4, 4, 1, 2, 3, 1, 4, 3, 4, 0, 1, 4, 4, 1, 4, 0, 3, 2, 4, 2, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 3, 0, 2, 0, 4, 4, 2, 4, 4, 3, 4, 1, 1, 3, 2, 3, 3, 3, 3, 4, 4, 2, 1, 2, 0, 4, 1, 4, 0, 1, 2, 3, 3, 2, 1, 1, 2, 4, 2, 1, 2, 2, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 2, 3, 0, 4, 2, 1, 0, 1, 1, 2, 3, 1, 0, 0, 3, 3, 1, 3, 2, 2, 1, 4, 2, 0, 3, 0, 0, 0, 2, 0, 4, 1, 2, 3, 4, 2, 1, 1, 3, 4, 4, 4, 1, 2, 3, 0, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 4, 4, 2, 2, 4, 0, 0, 0, 4, 3, 2, 2, 1, 3, 4, 2, 1, 4, 4, 1, 0, 2, 2, 3, 1, 3, 4, 4, 2, 1, 4, 0, 3, 3, 3, 1, 1, 2, 4, 1, 4, 0, 3, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 3, 1, 1, 4, 2, 3, 1, 2, 3, 2, 2, 1, 2, 1, 3, 4, 2, 4, 4, 3, 4, 3, 4, 3, 2, 2, 4, 1, 1, 1, 1, 2, 3, 1, 2, 4, 1, 3, 3, 3, 3, 4, 3 ] last modified: 2009-12-14
Lb(55,8) = 34 is found by shortening of: Lb(56,9) = 34 is found by truncation of: Lb(57,9) = 35 MST Ub(55,8) = 39 follows by a one-step Griesmer bound from: Ub(15,7) = 7 is found by considering shortening to: Ub(13,5) = 7 is found by considering truncation to: Ub(12,5) = 6 DL
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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