lower bound: | 136 |
upper bound: | 140 |
Construction of a linear code [216,8,136] over GF(3): [1]: [218, 8, 138] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 1, 0, 2, 1, 1, 1, 0, 2, 1, 2, 2, 2, 2, 1, 2, 0, 0, 1, 2, 1, 2, 0, 0, 1, 2, 0, 0, 0, 0, 1, 2, 1, 0, 0, 2, 1, 1, 0, 2, 0, 2, 0, 1, 2, 1, 0, 0, 0, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 2, 0, 2, 1, 1, 0, 2, 1, 1, 0, 2, 1, 2, 0, 0, 1, 0, 0, 1, 1, 2, 2, 0, 1, 0, 1, 2, 0, 2, 0, 1, 2, 1, 2, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 1, 0, 0, 0, 0, 2, 2, 2, 0, 1, 1, 0, 2, 2, 1, 1, 2, 2, 0, 1, 0, 2, 1, 1, 2, 1, 2, 0, 1, 0, 1, 2, 0, 2, 1, 1, 2, 1, 2, 1, 0, 0, 2, 2, 0, 2, 1, 1, 0, 1, 1, 2, 0, 1, 2, 0, 1, 0, 0, 0, 0, 2, 2, 2, 0, 1, 1, 1, 0, 2, 0, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 1, 2, 2, 1, 1, 0, 0, 1, 1, 1, 2, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 1 ] [ 0, 1, 0, 0, 0, 0, 2, 2, 2, 1, 0, 2, 0, 1, 0, 0, 2, 1, 1, 1, 2, 1, 0, 1, 2, 0, 0, 2, 2, 0, 1, 0, 2, 0, 0, 2, 0, 0, 2, 2, 0, 2, 1, 0, 2, 1, 0, 2, 1, 0, 1, 2, 1, 2, 2, 1, 0, 2, 2, 2, 0, 1, 2, 2, 0, 1, 0, 2, 2, 2, 0, 1, 2, 1, 2, 0, 0, 2, 1, 2, 0, 1, 2, 0, 0, 1, 1, 0, 0, 1, 0, 0, 2, 2, 0, 1, 2, 1, 0, 0, 1, 0, 0, 1, 1, 2, 1, 2, 0, 2, 2, 2, 0, 1, 1, 2, 1, 0, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 1, 2, 2, 0, 2, 0, 1, 2, 2, 0, 2, 1, 1, 0, 1, 0, 1, 0, 0, 2, 0, 0, 1, 2, 1, 2, 1, 2, 0, 1, 1, 2, 0, 2, 2, 2, 0, 2, 2, 0, 0, 1, 2, 0, 2, 1, 1, 2, 2, 2, 1, 2, 0, 1, 0, 2, 2, 2, 2, 1, 2, 2, 0, 2, 1, 1, 0, 1, 0, 1, 2, 0, 1, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 1, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 2, 1, 0, 0, 2, 1, 2, 1, 0, 1, 2, 0, 0, 1, 1, 2, 2, 1, 0, 2, 1, 0, 2, 1, 0, 2, 0, 1, 1, 2, 1, 0, 0, 0, 1, 1, 2, 0, 1, 2, 0, 1, 0, 1, 2, 2, 1, 1, 0, 0, 2, 0, 2, 2, 1, 1, 2, 0, 1, 2, 2, 2, 2, 2, 0, 1, 2, 0, 1, 1, 0, 0, 1, 0, 2, 0, 0, 2, 1, 1, 2, 2, 0, 2, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 0, 1, 1, 2, 2, 1, 1, 1, 2, 2, 0, 1, 0, 1, 1, 2, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 2, 0, 0, 1, 2, 2, 1, 2, 2, 0, 0, 0, 2, 2, 1, 1, 0, 2, 2, 1, 2, 1, 2, 0, 2, 2, 0, 2, 0, 1, 0, 1, 0, 0, 0, 1, 2, 1, 2, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 2, 0, 0, 1, 0, 2, 2, 1, 1, 0, 2, 1, 2, 1, 0, 0, 0, 1, 2, 2, 1, 0, 0 ] [ 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 1, 1, 2, 0, 2, 1, 2, 0, 0, 2, 1, 2, 1, 2, 1, 0, 2, 0, 1, 0, 2, 2, 2, 0, 1, 1, 2, 1, 1, 0, 1, 0, 1, 2, 2, 2, 0, 0, 2, 1, 1, 2, 0, 1, 0, 1, 1, 0, 1, 1, 1, 2, 2, 0, 1, 1, 2, 0, 0, 1, 2, 1, 0, 0, 1, 0, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 0, 1, 1, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 1, 1, 2, 2, 1, 0, 1, 2, 2, 2, 0, 1, 2, 2, 1, 0, 2, 1, 2, 0, 2, 0, 2, 2, 0, 2, 2, 2, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 1, 2, 2, 0, 2, 1, 0, 2, 0, 0, 0, 2, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 0, 1, 2, 2, 1, 0, 1, 0, 2, 1, 2, 0, 2, 2, 1, 0, 2, 1, 0, 1, 2, 0, 2, 0, 0, 0, 0, 1, 0, 0, 2, 1, 2, 1, 1, 0, 1, 0, 1, 1, 2, 0, 2, 1, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 2, 2, 1, 0, 0, 1, 2, 2, 0, 1, 0, 2, 2, 0, 2, 1, 1, 2, 2, 2, 2, 1, 0, 0, 1, 1, 0, 2, 1, 0, 2, 2, 0, 0, 2, 1, 1, 1, 1, 1, 0, 1, 1, 2, 0, 1, 1, 0, 0, 0, 2, 1, 1, 2, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 1, 2, 2, 0, 1, 0, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 1, 1, 0, 0, 2, 1, 2, 2, 2, 2, 0, 0, 2, 2, 1, 1, 0, 0, 0, 1, 0, 2, 1, 1, 1, 2, 2, 0, 1, 0, 0, 2, 0, 1, 0, 2, 2, 2, 0, 1, 2, 1, 0, 1, 1, 2, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 1, 1, 0, 2, 1, 1, 2, 1, 0, 2, 0, 1, 2, 0, 1, 2, 2, 1, 2, 2, 0, 1, 1, 0, 2, 2, 0, 1, 1, 2, 2, 1, 0, 2, 0, 0, 2, 1, 1, 2, 0, 0, 0, 2, 0, 1, 1, 0, 1, 2, 2, 1, 1, 1, 1, 0, 0, 2, 2, 1, 0, 1, 0, 1, 2, 2, 1, 1, 1, 2, 0, 1, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 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, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 0, 1 ] [ 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, 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, 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, 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, 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, 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, 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, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 0, 0 ] [2]: [216, 8, 136] Linear Code over GF(3) Puncturing of [1] at { 217 .. 218 } last modified: 2012-03-29
Lb(216,8) = 135 BZ Ub(216,8) = 140 follows by a one-step Griesmer bound from: Ub(75,7) = 46 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
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