lower bound: | 36 |
upper bound: | 38 |
Construction of a linear code [66,10,36] over GF(3): [1]: [66, 10, 36] Linear Code over GF(3) Code found by Nicola Pace Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 2, 0, 1, 2, 0, 0, 1, 0, 2, 0, 1, 1, 2, 1, 0, 0, 2, 2, 0, 0, 2, 2, 2, 1, 1, 0, 0, 2, 2, 1, 2, 0, 1, 1, 2, 1, 1, 0, 2, 2, 1, 0, 1, 0, 0, 0, 2, 2, 0, 2, 0, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 1, 1, 2, 0, 0, 2, 1, 2, 2, 2, 1, 2, 0, 0, 2, 0, 0, 0, 2, 1, 2, 2, 2, 2, 2, 0, 1, 2, 1, 1, 1, 0, 1, 1, 2, 1, 1, 1, 0, 2, 2, 2, 1, 2, 2, 0, 0, 2, 2, 1, 2, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 2, 1, 0, 2, 0, 0, 0, 1, 1, 0, 0, 1, 2, 2, 0, 0, 2, 1, 2, 1, 1, 0, 1, 1, 1, 2, 1, 1, 2, 0, 2, 2, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2, 1, 0, 2, 1, 2, 0, 0, 1, 0, 0 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 0, 1, 1, 0, 0, 2, 0, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 1, 2, 2, 1, 1, 0, 0, 2, 0, 1, 0, 1, 1, 2, 0, 1, 2, 1, 1, 0, 2, 0, 0, 1, 0, 1, 2, 1, 1, 2, 2, 0, 1, 0, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 1, 1, 1, 2, 0, 2, 1, 2, 0, 2, 1, 2, 2, 0, 0, 1, 0, 0, 1, 0, 1, 1, 2, 0, 0, 1, 0, 2, 2, 0, 1, 0, 1, 0, 1, 1, 0, 0, 1, 1, 2, 0, 0, 0, 1, 1, 2, 2, 2, 1, 0, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 2, 2, 2, 0, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 0, 1, 2, 1, 0, 1, 2, 2, 0, 1, 1, 2, 1, 1, 1, 1, 0, 2, 0, 0, 2, 2, 2, 2, 1, 2, 1, 0, 0, 2, 0, 2, 0, 2, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 2, 0, 1, 0, 2, 2, 1, 2, 0, 2, 0, 1, 2, 1, 1, 0, 0, 1, 0, 1, 2, 1, 2, 1, 0, 2, 0, 2, 0, 1, 0, 2, 2, 2, 1, 2, 1, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 1, 0, 2, 0, 1, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 2, 0, 1, 0, 2, 0, 1, 1, 1, 1, 0, 2, 1, 1, 2, 2, 1, 2, 0, 1, 0, 1, 2, 0, 1, 1, 0, 1, 0, 2, 0, 0, 1, 0, 2, 2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 0, 1, 0, 2, 2, 0, 1, 0, 2, 2, 0, 0, 1, 2, 0, 0, 2, 0, 2, 2, 2, 0, 0, 0, 1, 1, 1, 2, 1, 1, 0, 1, 1, 1, 2, 0, 1, 0, 2, 0, 1, 2, 1, 1, 0, 2, 0, 2, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 1, 0, 1, 1, 2, 0, 2, 0, 1, 2, 2, 2, 2, 1, 0, 1, 1, 2, 2, 0, 0, 0, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 2, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 2, 0, 2, 0 ] last modified: 2013-12-12
Lb(66,10) = 34 is found by shortening of: Lb(67,11) = 34 is found by truncation of: Lb(69,11) = 36 Bou Ub(66,10) = 38 follows by a one-step Griesmer bound from: Ub(27,9) = 12 is found by construction B: [consider deleting the (at most) 6 coordinates of a word in the dual]
Notes
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