lower bound: | 138 |
upper bound: | 142 |
Construction of a linear code [219,8,138] over GF(3): [1]: [219, 8, 138] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 0, 1, 2, 1, 2, 2, 0, 2, 2, 0, 2, 1, 1, 1, 0, 1, 0, 1, 0, 2, 1, 0, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0, 2, 1, 2, 2, 0, 2, 2, 2, 1, 0, 1, 2, 2, 1, 0, 1, 1, 2, 0, 0, 1, 0, 1, 1, 0, 0, 2, 2, 0, 1, 1, 1, 2, 2, 0, 2, 1, 1, 2, 1, 1, 1, 2, 0, 0, 2, 2, 1, 2, 0, 2, 2, 2, 1, 0, 2, 0, 0, 2, 0, 2, 1, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 2, 0, 1, 2, 0, 2, 0, 1, 2, 2, 2, 2, 1, 0, 1, 2, 1, 1, 1, 1, 1, 0, 2, 0, 1, 2, 0, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 0, 1, 2, 0, 1, 1, 1, 1, 1, 2, 0, 0, 0, 1, 1, 0, 1, 1, 2, 1, 0, 0, 2, 1, 2, 1, 0, 0, 2, 1 ] [ 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 2, 1, 2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 0, 2, 2, 2, 2, 2, 0, 0, 2, 2, 1, 1, 2, 0, 2, 1, 1, 1, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 0, 0, 1, 2, 1, 2, 0, 1, 0, 0, 2, 1, 1, 2, 1, 2, 0, 0, 1, 1, 1, 2, 0, 0, 0, 1, 2, 2, 1, 2, 0, 2, 0, 0, 2, 1, 0, 0, 2, 1, 1, 2, 0, 1, 1, 2, 2, 2, 0, 0, 0, 2, 1, 2, 0, 1, 0, 2, 1, 2, 0, 1, 1, 0, 0, 2, 2, 1, 0, 2, 1, 2, 1, 1, 0, 2, 0, 0, 1, 1, 0, 2, 1, 2, 0, 0, 0, 0, 0, 1, 1, 2, 2, 0, 1, 1, 1, 1, 2, 2, 0, 1, 0, 0, 2, 2, 2, 0, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 2, 2, 2, 0, 1, 0, 2, 1, 2, 1, 0, 0, 1, 0, 1, 1, 2, 1, 2, 2, 2, 0, 2, 1, 2, 1, 0, 0, 1, 0, 1, 0, 0, 2, 0, 1, 0, 2, 0, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 1, 1, 0, 0, 2, 2, 2, 1, 1, 0, 2, 0, 0, 2, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 2, 0, 0, 1, 1, 2, 0, 1, 2, 2, 2, 0, 1, 2, 1, 2, 2, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 0, 2, 1, 2, 0, 0, 1, 0, 2, 2, 1, 2, 0, 2, 2, 1, 2, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 2, 1, 1, 1, 2, 1, 0, 1, 2, 0, 2, 0, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 0, 0, 2, 1, 1, 1, 2, 0, 2, 2, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 2, 1, 0, 2, 2, 1, 1, 1, 1, 0, 1, 1, 0, 2, 1, 0, 2, 2, 2, 1, 1, 1, 2, 1, 0, 0, 2, 1, 1, 0, 1, 1, 2, 1, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 1, 0, 1, 1, 2, 1, 0, 2, 1, 0, 1, 1, 0, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 1, 2 ] [ 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 0, 1, 2, 1, 1, 2, 1, 1, 2, 1, 0, 0, 0, 1, 0, 1, 2, 1, 1, 2, 0, 2, 1, 0, 0, 1, 2, 1, 0, 0, 2, 2, 0, 2, 0, 2, 1, 0, 1, 0, 1, 0, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 0, 1, 1, 0, 1, 1, 2, 1, 2, 2, 0, 2, 0, 1, 1, 2, 2, 1, 0, 0, 0, 2, 1, 2, 2, 2, 1, 2, 0, 2, 2, 1, 2, 2, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 2, 0, 2, 0, 1, 2, 2, 1, 0, 0, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 2, 2, 0, 1, 0, 0, 2, 1, 0, 1, 0, 2, 0, 2, 1, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 1, 1, 1, 2, 0, 0, 0, 2, 2, 1, 2, 2, 0, 1, 2, 0, 0, 2, 1, 1, 0, 0, 0, 0, 2, 0, 2, 0, 0, 2, 1, 0, 2, 2, 2, 2, 1, 2, 1, 1, 0, 0, 0, 1, 0, 2, 1, 0, 0, 2, 2, 1, 0, 1, 2, 2, 2, 0, 1, 1, 1 ] [ 0, 0, 0, 0, 1, 0, 2, 2, 0, 0, 2, 2, 2, 1, 2, 0, 0, 2, 2, 2, 2, 2, 1, 0, 2, 0, 2, 1, 1, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 1, 2, 0, 1, 1, 2, 2, 0, 0, 1, 2, 2, 1, 1, 0, 0, 0, 2, 2, 1, 1, 0, 1, 0, 2, 1, 1, 0, 1, 2, 0, 0, 1, 2, 0, 1, 1, 1, 0, 1, 0, 1, 2, 2, 0, 1, 2, 2, 0, 1, 0, 1, 2, 2, 0, 1, 0, 2, 1, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 0, 2, 0, 2, 0, 1, 2, 0, 0, 2, 2, 2, 0, 2, 2, 1, 2, 1, 2, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 2, 2, 1, 0, 0, 1, 2, 1, 1, 2, 2, 0, 2, 2, 1, 1, 2, 2, 2, 1, 2, 0, 1, 1, 0, 0, 2, 0, 2, 2, 2, 0, 1, 1, 0, 2, 2, 1, 1, 2, 2, 0, 1, 0, 2, 2, 0, 0, 2, 1, 0, 2, 1, 2, 1, 2, 1, 0, 2, 1, 0, 2, 0, 1, 1, 0, 0, 2, 0, 2, 2, 1, 2, 0, 0, 2, 2, 1, 0, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 2, 1, 0, 2, 0, 2, 0, 1, 0, 0, 1, 0, 1, 2, 0, 1, 0, 2, 1, 2, 1, 2, 0, 1, 0, 2, 0, 1, 2, 2, 2, 2, 2, 0, 0, 1, 2, 1, 0, 1, 0, 2, 1, 1, 1, 2, 1, 1, 1, 1, 0, 1, 2, 1, 1, 0, 0, 0, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, 0, 1, 2, 0, 2, 2, 0, 0, 0, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 0, 2, 1, 1, 0, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 2, 0, 1, 1, 2, 0, 2, 1, 1, 0, 1, 2, 0, 1, 1, 1, 1, 2, 0, 1, 0, 1, 2, 2, 1, 2, 0, 2, 2, 2, 0, 1, 2, 1, 2, 0, 2, 1, 1, 2, 1, 1, 0, 0, 2, 2, 1, 1, 0, 2, 1, 0, 1, 1, 2, 1, 0, 1, 0, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 2, 2, 1, 0, 1, 2, 0, 1, 0, 1, 0, 1, 0, 1, 2, 1, 0, 0, 2, 0, 1, 0, 0, 1, 0, 2, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 2, 2, 1, 1, 0, 0, 1, 2, 0, 0, 2, 0, 2, 0, 1, 0, 1, 1, 0, 2, 0, 1, 0, 2, 0, 0, 2, 1, 0, 0, 2, 0, 0, 0, 1, 0, 2, 0, 2, 0, 0, 2, 2, 0, 0, 0, 2, 0, 1, 1, 0, 1, 0, 0, 2, 0, 2, 2, 0, 1, 2, 2, 1, 0, 0, 1, 2, 2, 1, 1, 1, 2, 1, 0, 0, 0, 1, 2, 1, 0, 2, 1, 2, 0, 0, 1, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 2, 2, 2, 2, 0, 1, 0, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 1, 1, 2, 2, 1, 0, 2, 2, 1, 2, 2, 1, 0, 1, 1, 1, 2, 2, 1, 0, 0, 2, 1, 1, 2, 1, 0, 1, 2, 2, 1, 2, 0, 1, 0, 2, 1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 2, 1, 2, 2, 2, 0, 0, 1, 1, 2, 1, 2, 0, 1, 0, 2, 0, 0, 2, 1, 1, 0, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 2, 0, 1, 0, 1, 0, 0, 2, 2, 0, 0, 1, 2, 0, 0, 1, 1, 0, 2, 1, 1, 2, 1, 2, 1, 0, 1, 0, 2, 0, 1, 0, 2, 0, 2, 1, 1, 2, 0, 1, 1, 2, 1, 1, 1, 0, 1, 2, 1, 2, 1, 1, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 2, 1, 2, 2, 1, 0, 2, 2, 0, 1, 1, 2, 1, 1, 2, 2, 0, 2, 0, 1, 1, 1, 0, 2, 0, 1, 2, 0, 2, 1, 1, 0, 0, 1, 0, 1, 0, 2, 1, 0, 0, 2, 2, 2, 2, 2, 1, 0, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 2, 0, 1, 1, 2, 2, 1, 2, 0, 1, 2, 2, 0, 2, 2, 0, 1, 0, 0, 0, 2, 2, 0, 1, 1, 1, 2, 2, 1, 2, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 2, 1, 1, 1, 0, 0, 0, 0, 2, 0, 2, 1, 0, 1, 2, 1, 1, 2, 0, 0, 1, 2, 1, 2, 0 ] last modified: 2008-11-06
Lb(219,8) = 137 is found by truncation of: Lb(220,8) = 138 BZ Ub(219,8) = 142 follows by a one-step Griesmer bound from: Ub(76,7) = 47 follows by a one-step Griesmer bound from: Ub(28,6) = 15 HHM
HHM: N. Hamada, T. Helleseth, H.M. Martinsen & Ø. Ytrehus, There is no ternary [28,6,16] code
Notes
|