lower bound: | 129 |
upper bound: | 135 |
Construction of a linear code [210,9,129] over GF(3): [1]: [210, 9, 129] 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, 1, 0, 2, 0, 2, 0, 0, 2, 0, 2, 1, 2, 0, 1, 0, 1, 0, 1, 1, 2, 2, 2, 0, 1, 1, 2, 1, 0, 2, 0, 1, 1, 2, 0, 2, 2, 2, 0, 0, 1, 0, 1, 1, 2, 1, 1, 0, 2, 2, 0, 0, 2, 2, 2, 2, 1, 0, 1, 1, 1, 2, 1, 2, 0, 2, 0, 2, 1, 1, 2, 2, 0, 2, 0, 1, 0, 0, 1, 0, 1, 0, 1, 1, 2, 2, 2, 0, 1, 0, 0, 0, 1, 2, 2, 2, 2, 0, 0, 0, 2, 1, 0, 1, 2, 1, 0, 2, 2, 2, 0, 2, 0, 2, 1, 0, 1, 0, 0, 2, 2, 2, 2, 2, 1, 0, 1, 2, 0, 1, 0, 0, 0, 1, 2, 1, 0, 0, 2, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 2, 1, 2, 1, 1, 2, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 1, 0, 2, 2, 1, 1, 2, 1, 2, 0, 1, 1, 0, 0, 2, 1, 2, 2, 2, 0, 2, 2, 1, 1, 0, 0, 0, 1, 0, 2, 1 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 2, 0, 0, 2, 2, 1, 1, 1, 0, 2, 2, 2, 1, 2, 2, 2, 0, 1, 1, 2, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 2, 1, 0, 1, 1, 1, 1, 1, 0, 2, 1, 2, 2, 0, 2, 2, 1, 1, 2, 2, 0, 0, 0, 2, 0, 2, 2, 1, 2, 2, 1, 2, 1, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 1, 1, 2, 0, 0, 0, 1, 1, 0, 0, 2, 2, 1, 0, 1, 1, 1, 2, 1, 2, 2, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 2, 2, 0, 2, 0, 1, 2, 0, 0, 2, 2, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 0, 1, 2, 1, 1, 1, 0, 0, 2, 0, 2, 1, 2, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 1, 2, 2, 0, 2, 0, 0, 2, 0, 2, 1, 2, 1, 0, 0, 2, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, 2, 1, 2, 2, 1, 2, 0, 0, 0, 1, 1, 0, 2, 0, 1, 1, 2, 2, 0, 0, 1, 2, 2, 1, 0, 1, 0, 2, 2, 1, 2, 0, 2, 1, 0, 2, 2, 1, 1, 2, 1, 0, 1, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 2, 0, 1, 1, 2, 0, 0, 0, 1, 1, 2, 0, 1, 1, 0, 0, 1, 2, 2, 1, 1, 0, 0, 1, 2, 0, 0, 1, 0, 2, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 0, 0, 1, 2, 0, 0, 0, 0, 2, 1, 2, 1, 1, 1, 1, 0, 2, 2, 1, 1, 1, 1, 2, 2, 0, 1, 1, 2, 0, 1, 0, 0, 2, 2, 1, 0, 2, 2, 1, 2, 0, 0, 2, 1, 0, 1, 1, 2, 1, 0, 2, 0, 0, 2, 1, 0, 1, 2, 1, 1, 2, 0, 0, 0, 1, 2, 0, 2, 2, 1, 0, 0, 0, 2, 2, 1, 1, 0, 0, 1, 1, 1, 2, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 1, 1, 2, 2, 0, 2, 1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 1, 1, 2, 2, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 1, 2, 0, 2, 2, 2, 0, 2, 2, 0, 1, 1, 1, 2, 0, 0, 2, 1, 0, 1, 0, 1, 1, 0, 1, 2, 2, 1, 1, 0, 0, 0, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 0, 2, 2, 2, 1, 2, 0, 0, 1, 0, 2, 2, 0, 1, 2, 0, 0, 1, 1, 2, 2, 2, 1, 2, 0, 2, 2, 0, 1, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 1, 0, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 2, 1, 2, 1, 2, 1, 1, 0, 1, 0, 1, 2, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 2, 0, 2, 1, 0, 1, 2, 0, 1, 0, 2, 0, 2, 1, 2, 1, 2, 2, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 1, 0, 0, 2, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 1, 1, 1, 0, 1, 1, 2, 2, 0, 2, 1, 2, 2, 0, 1, 1, 2, 2, 1, 0, 1, 0, 1, 2, 1, 0, 2, 0, 2, 1, 1, 2, 2, 2, 1, 0, 2, 2, 2, 0, 0, 1, 0, 1, 2, 2, 0, 2, 2, 2, 0, 0, 0, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 0, 0, 2, 1, 0, 2, 0, 2, 2, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 1, 2, 2, 2, 0, 1, 1, 1, 1, 2, 1, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 1, 2, 0, 0, 0, 1, 1, 0, 0, 1, 2, 0, 2, 2, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 2, 0, 2, 0, 1, 2, 1, 0, 2, 1, 2, 1, 1, 2, 2, 2, 2, 0, 1, 2, 0, 0, 1, 1, 0, 1, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 1, 2, 0, 1, 1, 2, 1, 1, 0, 0, 2, 2, 1, 1, 0, 2, 0, 1, 0, 2, 0, 2, 1, 0, 1, 2, 1, 2, 2, 0, 0, 2, 1, 1, 0, 1, 1, 0, 0, 0, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 0, 0, 2, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 0, 1, 2, 0, 0, 1, 2, 2, 1, 1, 2, 0, 0, 0, 1, 2, 0, 1, 0, 2, 2, 0, 0, 0, 1, 0, 2, 2, 0, 2, 0, 0, 2, 0, 1, 2, 0, 2, 2, 2, 2, 0, 2, 0, 1, 1, 2, 2, 1, 1, 0, 0, 2, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 2, 1, 2, 0, 1, 1, 2, 2, 1, 2, 2, 0, 1, 1, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 2, 0, 1, 2, 2, 2, 0, 2, 1, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 1, 1, 1, 1, 1, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 2, 2, 0, 1, 2, 1, 1, 1, 0, 2, 1, 0, 0, 1, 1, 2, 0, 1, 2, 1, 1, 0, 2, 1, 1, 1, 0, 0, 2, 1, 2, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 0, 0, 0, 2, 1, 0, 2, 0, 1, 1, 0, 2, 2, 1, 0, 1, 1, 2, 2, 2, 0, 1, 2, 0, 2, 0, 0, 2, 2, 1, 2, 2, 1, 1, 2, 0, 0, 0, 2, 0, 2, 2, 2, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 0, 2, 2, 0, 1, 1, 2, 2, 0, 2, 0, 2, 0, 2, 0, 0, 2, 1, 0, 2, 1, 2, 2, 1, 0, 2, 0, 2, 1, 2, 2, 0, 2, 0, 1, 0, 0, 1, 1, 0, 2, 2, 0, 0, 0, 1, 0, 1, 1, 0, 2, 2, 2, 2, 2, 0, 0, 1, 2, 0, 0, 2, 2, 1, 1, 1, 1, 0, 2, 0, 1, 1, 0, 1, 0, 1, 2, 2, 2, 0, 1, 1, 2, 1, 2, 0, 1, 0, 0, 2, 2, 2, 1, 2, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 0, 2, 2, 2, 2, 2, 0, 1, 1, 2, 0, 0, 2, 2, 2, 1, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 1, 0, 0, 1, 1, 1, 1, 2, 0, 1, 2, 1, 1, 2, 2, 1, 0, 0, 2, 2, 1, 2, 0, 1, 0, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0, 1, 0, 2, 1, 2, 1, 0, 1, 1, 2, 0, 2, 2, 0, 0, 1, 2, 2, 1, 0, 0, 2, 2, 1, 2, 1, 0, 1, 1, 0, 2, 1, 2, 2, 0, 2, 1, 0, 0, 1, 2, 1, 0, 1, 2, 2, 1, 0, 2, 0, 1, 2, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 2, 2, 1, 2, 1, 1, 2, 2, 2, 2, 0, 2, 2, 2, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 2, 0, 0, 0, 0, 2, 1, 2, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 2, 0, 2, 0, 2, 1, 1, 2, 2, 2, 0, 1, 0, 1, 1, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 0, 2, 2, 1, 0, 2, 1, 2, 0, 2, 2, 0, 1, 1, 2, 2, 0, 2, 1, 0, 1, 1, 1, 1, 2, 2, 2, 1, 2, 0, 2, 2, 0, 0, 2, 0, 1, 0, 2, 1, 1, 2, 0, 2, 0, 2, 2, 1, 0, 2, 0, 0, 2, 2, 2, 2, 1, 1, 0, 1, 2, 1, 0, 2, 0, 1, 2, 2, 0, 1, 0, 0, 2, 1, 2, 2, 1, 1, 0, 2, 2, 2, 0, 0, 1, 1, 2, 2, 0, 1, 0, 0, 1, 2, 0, 2, 2, 1, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 1, 2, 0, 2, 1, 0, 2, 2, 1, 1, 1, 2, 1, 0, 2, 0, 0, 1, 1, 1, 2, 2, 0, 0, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 0, 2, 0, 0, 0, 2, 2, 2, 0, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 0, 2, 2, 2, 0 ] last modified: 2008-10-21
Lb(210,9) = 127 is found by shortening of: Lb(211,10) = 127 is found by truncation of: Lb(212,10) = 128 MSY Ub(210,9) = 135 follows by a one-step Griesmer bound from: Ub(74,8) = 45 follows by a one-step Griesmer bound from: Ub(28,7) = 15 is found by considering shortening to: Ub(26,5) = 15 is found by construction B: [consider deleting the (at most) 3 coordinates of a word in the dual]
Notes
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