lower bound: | 30 |
upper bound: | 32 |
Construction of a linear code [57,10,30] over GF(3): [1]: [57, 10, 30] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 1, 2, 1, 2, 1, 0, 1, 2, 1, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 1, 1, 2, 1, 0, 1, 0, 2, 2, 0, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 0 ] [ 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 0, 0, 2, 1, 2, 0, 1, 1, 1, 2, 2, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 1, 0, 1, 1, 2, 0, 2, 1, 1, 0, 0, 2, 1, 2, 2 ] [ 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 1, 0, 0, 1, 2, 2, 1, 1, 2, 2, 2, 0, 2, 0, 0, 2, 0, 1, 2, 1, 1, 1, 2, 1, 0, 1, 0, 1, 2, 2, 1, 0, 1, 0, 2, 1, 1, 1, 2, 0, 1, 2 ] [ 0, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 2, 1, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 2, 1, 0, 2, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 2, 2 ] [ 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 2, 1, 0, 0, 2, 2, 0, 2, 1, 2, 1, 0, 0, 2, 1, 2, 1, 2, 1, 2, 2, 2, 0, 2, 2, 1, 2, 1, 1, 0, 0, 0, 2, 2, 1, 2, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 0, 2, 1, 0, 2, 2, 0, 1, 0, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 2, 0, 0, 0, 0, 1, 1, 2, 0, 0, 1, 0, 1, 1, 1, 1, 1, 2, 0, 1, 2, 1, 2, 2, 2, 1, 0, 2, 2, 1, 2, 0, 1, 1, 1, 0, 2, 0, 2, 0, 0, 0, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 0, 0, 1, 2, 1, 2, 2, 2, 1, 2, 0, 0, 2, 1, 2, 1, 0, 0, 0, 1, 0, 2, 2, 1, 1, 1, 2, 0, 0, 2, 2, 1, 0, 0, 2, 1, 0, 0, 2, 1, 2, 1, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 2, 1, 2, 2, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 2, 1, 0, 0, 1, 0, 1, 0, 1, 1, 0, 2, 0, 0, 1, 1, 2, 2, 1, 2, 2, 2, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 1, 2, 1, 1, 2, 2, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 2, 2, 2, 1, 2 ] last modified: 2009-08-13
Lb(57,10) = 29 is found by truncation of: Lb(58,10) = 30 XX Ub(57,10) = 32 is found by considering shortening to: Ub(55,8) = 32 Gur
XX:
Notes
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