lower bound: | 144 |
upper bound: | 146 |
Construction of a linear code [225,8,144] over GF(3): [1]: [225, 8, 144] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 2, 2, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 2, 2, 1, 1, 2, 1, 1, 0, 0, 2, 1, 1, 2, 0, 1, 1, 0, 2, 2, 1, 1, 0, 2, 1, 1, 2, 2, 2, 2, 0, 1, 0, 2, 1, 0, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 0, 2, 2, 0, 0, 0, 1, 2, 0, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 0, 1, 1, 2, 1, 0, 2, 1, 2, 1, 2, 2, 1, 1, 0, 1, 2, 2, 0, 0, 2, 0, 0, 1, 0, 2, 1, 2, 2, 0, 0, 1, 0, 0, 1, 0, 1, 1, 2, 2, 1, 1, 2, 0, 1, 2, 1, 2, 1, 0, 2, 1, 1, 2, 1, 0, 2, 2, 2, 2, 1, 0, 0, 1, 1, 0, 2, 0, 2, 0, 2, 2, 0, 1, 1, 1, 1, 0, 2, 0, 0, 1, 1, 1, 1, 2, 1, 2, 0, 0, 2, 1, 1, 2, 1, 0, 1, 0, 2, 2, 0, 0, 2, 1, 0, 1, 0, 0, 2, 1, 2, 2, 0, 2, 1, 0, 0, 1, 2, 2, 2, 2, 0, 2, 0, 0, 2, 1, 1, 2, 0, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 2, 0, 2, 0, 0, 1, 1, 0, 1, 2, 2, 0, 2, 0, 1, 0, 0, 2, 1, 1, 2, 0, 0, 1, 1, 1, 2, 2, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 1, 2, 0, 2, 1, 1, 0, 0, 2, 0, 2, 0, 1, 0, 2, 2, 1, 0, 2, 2, 0, 1, 2, 0, 0, 1, 2, 0, 2, 1, 2, 1, 0, 2, 1, 2, 0, 2, 0, 2, 1, 1, 1, 2, 2, 2, 2, 1, 0, 0, 1, 0, 2, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 1, 0, 1, 2, 2, 0, 1, 0, 1, 0, 2, 0, 1, 2, 0, 0, 0, 1, 2, 1, 2, 2, 0, 2, 0, 1, 2, 1, 2, 1, 2, 2, 2, 1, 0, 2, 2, 2, 0, 2, 0, 2, 0, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 0, 2, 0, 2, 2, 2, 0, 1, 2, 1, 0, 2, 0, 0, 1, 1, 1, 1, 1, 2, 1, 1, 0, 2, 1, 2, 2, 2, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 2, 1, 1, 2, 0, 0, 0, 2, 2, 0, 1, 0, 1, 2, 2, 1, 0, 0, 2, 0, 2 ] [ 0, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 1, 0, 1, 0, 0, 1, 2, 2, 0, 2, 0, 0, 1, 1, 0, 2, 0, 0, 1, 0, 2, 0, 0, 2, 2, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 0, 1, 2, 0, 2, 0, 2, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2, 0, 0, 2, 0, 0, 1, 1, 2, 0, 0, 0, 0, 1, 0, 1, 2, 1, 0, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 2, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 2, 1, 1, 1, 2, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 2, 2, 1, 2, 0, 0, 2, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, 0, 2, 1, 1, 2, 2, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 1, 1, 2, 1, 2, 0, 0, 2, 0, 1, 1, 2, 2, 2, 1, 1, 2, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 1, 1, 0, 2, 2, 2, 0, 0, 1, 1, 1, 1, 2, 1, 1, 2, 0, 1, 2, 2, 0, 0, 0, 0, 1, 0, 2, 1, 2, 0, 1, 2, 2, 2, 2, 0, 0, 2, 1, 0, 2, 1, 2, 0, 1, 0, 2, 1, 0, 2, 1, 1, 1, 0, 0, 2, 2, 2, 2, 1, 0, 1, 2, 0, 0, 0, 0, 1, 2, 2, 0, 2, 0, 0, 1, 1, 2, 2, 2, 1, 0, 0, 2, 2, 2, 2, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 2, 2, 0, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 1, 2, 0, 1, 0, 0, 2, 2, 0, 1, 1, 2, 2, 2, 2, 0, 1, 0, 0, 1, 1, 1, 2, 1, 0, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2, 0, 1, 0, 0, 1, 1, 2, 0, 0, 2, 1, 0, 2, 1, 1, 2, 2, 2, 0, 0, 1, 1, 0, 1, 1, 2, 2, 2, 0, 0, 2, 1, 2, 1, 1, 0, 0, 2, 0, 0, 2, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 0, 1, 1, 0, 2, 2, 2, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 1, 2, 2, 2, 1, 0, 1, 0, 0, 1, 0, 2, 1, 1, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 0, 2, 2, 0, 0, 0, 2, 1, 1, 1, 2, 1, 0, 2, 1, 1, 1, 1, 0, 1, 2, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 2, 2, 1, 0, 1, 1, 1, 0, 0, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 2, 0, 1, 0, 0, 1, 2, 0, 0, 1, 2, 2, 2, 2, 0, 1, 2, 0, 0, 0, 0, 1, 1, 2, 0, 1, 2, 1, 1, 0, 1, 0, 1, 2, 2, 2, 0, 1, 1, 2, 2, 2, 1, 0, 0, 2, 2, 2, 1, 2, 2, 2, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 1, 0, 1, 0, 1, 2, 2, 2, 1, 0, 0, 2, 0, 1, 2, 0, 2, 2, 1, 2, 2, 0, 0, 2, 1, 0, 0, 2, 2, 1, 1, 2, 2, 0, 2, 2, 0, 1, 2, 1, 0, 1, 0, 2, 2, 1, 0, 2, 2, 1, 0, 1, 0, 2, 1, 2, 0, 1, 0, 1, 2 ] [ 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 0, 2, 2, 0, 1, 1, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 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, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ] last modified: 2012-03-29
Lb(225,8) = 141 is found by truncation of: Lb(228,8) = 144 BKW Ub(225,8) = 146 follows by a one-step Griesmer bound from: Ub(78,7) = 48 follows by a one-step Griesmer bound from: Ub(29,6) = 16 is found by considering truncation to: Ub(28,6) = 15 HHM
HHM: N. Hamada, T. Helleseth, H.M. Martinsen & Ø. Ytrehus, There is no ternary [28,6,16] code
Notes
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