lower bound: | 48 |
upper bound: | 49 |
Construction of a linear code [81,9,48] over GF(3): [1]: [81, 9, 48] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 1, 2, 1, 1, 1, 1, 2, 0, 0, 1, 1, 2, 1, 0, 2, 2, 0, 1, 0, 2, 1, 1, 2, 2, 0, 2, 1, 1, 2, 2, 0, 0, 1, 0, 0, 1, 0, 0, 2, 2, 1, 1, 2, 1, 0, 0, 2, 2, 0, 1, 2, 1, 1, 1, 2, 0, 1, 0, 0, 2, 2 ] [ 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 0, 1, 0, 0, 0, 1, 0, 2, 2, 1, 2, 1, 1, 1, 2, 1, 0, 0, 2, 0, 2, 2, 2, 0, 2, 1, 1, 2, 0, 2, 2, 2, 0, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 2 ] [ 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 2, 2, 0, 2, 2, 0, 2, 2, 0, 0, 0, 1, 2, 2, 0, 1, 1, 2, 1, 1, 2, 0, 0, 1, 2, 2, 0, 1, 1, 2, 0, 0, 1, 2, 2, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 2, 0, 0, 0, 1, 1, 1, 2, 0, 0, 1, 1, 1, 2, 2, 2, 0 ] [ 0, 0, 0, 1, 0, 2, 0, 1, 2, 0, 1, 2, 0, 0, 0, 1, 0, 2, 1, 0, 2, 0, 1, 2, 0, 0, 0, 0, 2, 1, 2, 0, 1, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0, 1, 2, 1, 2, 0, 1, 1, 1, 2, 1, 0, 2, 0, 1, 2, 2, 2, 0, 2, 1, 2, 1, 0, 1, 2, 0, 1, 1, 1, 0, 0, 0, 1, 0, 2, 0, 1, 2 ] [ 0, 0, 0, 0, 1, 2, 0, 2, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 2, 2, 0, 1, 2, 1, 0, 0, 0, 0, 2, 0, 1, 1, 0, 2, 0, 0, 0, 2, 0, 1, 1, 0, 2, 2, 2, 2, 1, 2, 0, 0, 2, 1, 1, 1, 1, 2, 0, 1, 0, 2, 1, 1, 1, 1, 2, 0, 1, 0, 2, 1, 0, 0, 0, 1, 2, 0, 2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 2, 0, 1, 2, 1, 2, 0, 2, 1, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 2, 2, 2, 2, 2, 2, 0, 1, 2, 2, 0, 1, 2, 0, 1, 2, 1, 0, 1, 0, 2, 1, 0, 2, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 2, 1, 2, 0, 0, 1, 2, 2, 1, 0, 0, 2, 1, 2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 1, 1, 2, 2, 2, 0, 2, 1, 1, 0, 2, 2, 1, 0, 1, 0, 2, 1, 0, 2, 1, 0, 2, 0, 2, 1, 2, 1, 0, 1, 0, 2, 0, 1, 2, 2, 0, 1, 1, 2, 0, 1, 2, 0, 2, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 0, 1, 1, 2, 0, 0, 1, 2, 0, 1, 2, 0, 1, 2, 2, 0, 1, 0, 1, 2, 1, 2, 0, 0, 2, 1, 1, 0, 2, 2, 1, 0, 0, 2, 1, 2, 1, 0, 1, 0, 2, 2, 1, 0, 2, 1, 0, 2, 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, 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, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2 ] last modified: 2003-09-25
Lb(81,9) = 48 BE Ub(81,9) = 49 follows by a one-step Griesmer bound from: Ub(31,8) = 16 is found by considering shortening to: 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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