lower bound: | 27 |
upper bound: | 29 |
Construction of a linear code [54,11,27] over GF(3): [1]: [54, 11, 27] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 2, 2, 2, 0, 2, 0, 1, 0, 0, 1, 0, 2, 2, 2, 0, 2, 1, 2, 2, 2, 1, 1, 0, 0, 2, 2, 2, 1, 2, 1, 0, 2, 2, 0, 2, 2, 2, 2, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 2, 1, 1, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 1, 2, 1, 1, 2, 0, 0, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 0, 2, 1, 0, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 2, 1, 0, 0, 2, 0, 0, 0, 2, 2, 1, 0, 2, 0, 0, 1, 2, 0, 0, 1, 1, 0, 0, 2, 1, 0, 0, 1, 1, 1, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 2, 0, 0, 0, 2, 1, 0, 1, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 1, 0, 1, 2, 2, 2, 1, 2, 0, 0, 1, 1, 0, 2, 0, 1, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 1, 1, 1, 0, 0, 1, 2, 0, 1, 0, 1, 0, 0, 0, 2, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 2, 1, 0, 1, 1, 0, 0, 2, 0, 1, 2, 1, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 1, 2, 1, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 1, 0, 2, 0, 2, 1, 1, 2, 0, 0, 2, 1, 0, 0, 1, 1, 1, 1, 2, 1, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 1, 2, 0, 0, 2, 2, 0, 1, 2, 0, 0, 1, 0, 2, 0, 0, 1, 0, 2, 1, 1, 1, 0, 2, 0, 2, 0, 2, 1, 2, 1, 2, 2, 0, 0, 0, 1, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2, 2, 2, 2, 1, 0, 2, 2, 1, 0, 2, 0, 0, 0, 0, 2, 2, 1, 2, 0, 2, 1, 1, 2, 2, 0, 1, 2, 1, 2, 2, 0, 1, 1, 2, 1, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 1, 2, 1, 0, 2, 1, 1, 1, 0, 2, 0, 1, 2, 0, 0, 0, 0, 1, 1, 2, 0, 0, 2, 0, 2, 0, 2, 0, 1, 0, 2, 0, 1, 2, 2, 1, 2, 0, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 1, 1, 2, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 2, 0, 2, 0, 1, 1, 2, 1, 0, 1, 0, 0, 2, 2, 2, 0, 0, 1, 2, 1, 0, 2, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 2, 2, 0 ] last modified: 2009-06-05
Lb(54,11) = 26 is found by shortening of: Lb(55,12) = 26 is found by truncation of: Lb(56,12) = 27 ARS Ub(54,11) = 29 is found by considering truncation to: Ub(53,11) = 28 is found by construction B: [consider deleting the (at most) 6 coordinates of a word in the dual]
Notes
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