lower bound: | 105 |
upper bound: | 108 |
Construction of a linear code [168,8,105] over GF(3): [1]: [168, 8, 105] Linear Code over GF(3) Code found by Axel Kohnert and Johannes Zwanzger Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 1, 0, 0, 2, 0, 2, 1, 0, 1, 1, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 2, 1, 2, 0, 2, 0, 2, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 2, 2, 1, 1, 1, 1, 0, 1, 1, 2, 1, 2, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 0, 1, 1, 2, 0, 1, 2, 0, 2, 0, 1, 0, 2, 2, 1, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 2, 0, 0, 2, 1, 0, 1, 2, 2, 1, 0, 0, 2, 1, 1, 2, 2, 0, 0, 2, 0, 0, 0, 0, 1, 1, 2, 1, 1, 0, 1, 2, 2, 0, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 0, 0, 1, 0, 2, 1, 2, 0, 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 0, 0, 1, 2, 1, 0, 2, 2, 1, 0, 2, 1, 2, 2, 0, 1, 0, 2, 1, 0, 0, 0, 0, 2, 2, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 2, 0, 1, 0, 2, 2, 0, 1, 2, 2, 1, 2, 1, 1, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 0, 1, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 0, 1, 2, 1, 0, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 1, 2, 0, 2, 2, 2, 2, 1, 1, 0, 1, 2, 2, 1, 1, 0, 0, 1, 2, 0, 2, 0, 1, 0, 1, 2, 2, 2, 2, 2, 1, 0, 2, 1, 0, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 2, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 2, 0, 1, 2, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 1, 2, 1, 0, 0, 0, 2, 2, 0, 2, 1, 0, 2, 0, 2, 1, 2, 0, 0, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 0, 1, 2, 1, 0, 1, 1, 1, 1, 0, 0, 1, 2, 1, 2, 2, 0, 0, 1, 0, 0, 2, 0, 0, 2, 2, 0, 2, 2, 1, 1, 1, 2, 0, 2, 0, 2, 0, 1, 2, 1, 1, 2, 2, 0, 1, 0, 1, 1, 2, 2, 2, 1, 0, 0, 1, 1, 1, 2, 2, 2, 1, 0, 1, 0, 2, 0, 2, 0, 0, 2, 0, 1, 2, 0, 0, 0, 0, 2, 0, 1, 1, 0, 0, 2, 1, 0, 1, 0, 1, 0, 1, 1, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 2, 2, 0, 0, 1, 2, 2, 1, 2, 2, 0, 2, 0, 1, 0, 0, 2, 2, 1, 0, 0, 1, 2, 2, 0, 1, 1, 2, 0, 1, 2, 1, 0, 2, 2, 0, 2, 0, 1, 0, 2, 2, 2, 2, 2, 0, 2, 1, 0, 1, 1, 2, 2, 2, 2, 0, 2, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0, 1, 1, 2, 1, 1, 2, 1, 2, 1, 0, 2, 0, 2, 2, 1, 2, 2, 1, 1, 2, 1, 0, 0, 1, 1, 2, 2, 2, 2, 0, 1, 2, 1, 2, 2, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 1, 0, 1, 2, 1, 2, 1, 2, 2, 1, 0, 2, 1, 2, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 1, 2, 0, 1, 0, 0, 0, 1, 1, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 1, 1, 2, 1, 2, 1, 0, 1, 1, 0, 0, 2, 0, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 0, 2, 0, 2, 2, 1, 1, 0, 1, 2, 1, 2, 1, 0, 1, 0, 2, 1, 1, 2, 2, 2, 0, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 1, 0, 1, 2, 0, 0, 2, 0, 2, 2, 1, 0, 2, 0, 0, 1, 2, 0, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0, 1, 0, 2, 1, 1, 1, 2, 2, 0, 0, 2, 1, 1, 0, 2, 2, 0, 1, 0, 1, 0, 1, 1, 2, 1, 1, 0, 0, 2, 0, 1, 1, 0, 0, 2, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 2, 1, 2, 2, 0, 0, 0, 0, 2, 1, 2, 1, 1, 2, 0, 2, 0, 1, 0, 1, 2, 0, 2, 0, 2, 2, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 2, 1, 2, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 1, 0, 1, 0, 1, 1, 2, 2, 0, 2, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 1, 2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 0, 1, 1, 0, 1, 2, 1, 1, 1, 0, 1, 1, 2, 0, 0, 0, 2, 2, 0, 1, 1, 2, 1, 1, 0, 1, 0, 0, 0, 1, 2, 2, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 2, 0, 2, 1, 2, 0, 1, 2, 1, 1, 0, 0, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 1, 2, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 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, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 2, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 1, 2, 1, 2, 0, 0, 2 ] last modified: 2008-11-24
Lb(168,8) = 103 is found by truncation of: Lb(173,8) = 108 Koh Ub(168,8) = 108 follows by the Griesmer bound.
Notes
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