lower bound: | 44 |
upper bound: | 45 |
Construction of a linear code [75,8,44] over GF(3): [1]: [76, 8, 45] 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, 2, 2, 2, 0, 2, 1, 1, 0, 2, 1, 2, 1, 1, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 2, 2, 0, 2, 2, 1, 0, 1, 1, 2, 2, 1, 0, 0, 2, 0, 1, 2, 2, 1, 2, 0, 1, 0, 2, 1, 0, 1, 1, 0, 0, 0, 2, 0, 0, 1, 2, 2, 0, 0, 0, 0, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 2, 2, 2, 0, 1, 0, 0, 1, 2, 2, 0, 2, 1, 1, 1, 0, 1, 1, 1, 0, 2, 2, 0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 2, 2, 0, 2, 0, 1, 2, 0, 0, 1, 1, 1, 1, 1, 2, 0, 2, 1, 1, 2, 1, 2, 0, 1, 0, 1, 0, 2, 0, 1, 1 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 2, 2, 1, 1, 0, 1, 0, 1, 2, 0, 2, 2, 1, 1, 1, 2, 1, 0, 1, 2, 1, 1, 2, 2, 2, 0, 1, 1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 2, 0, 1, 1, 2, 1, 0, 1, 1, 2, 1, 2, 0, 2, 1, 0, 0, 0, 0, 2, 1, 1, 2, 0, 2, 0, 0, 2, 0, 2, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 1, 1, 2, 1, 0, 2, 1, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 1, 1, 0, 2, 0, 2, 0, 1, 0, 2, 1, 0, 1, 1, 1, 2, 0, 1, 0, 0, 1, 2, 0, 2, 2, 1, 2, 1, 0, 0, 1, 1, 0, 1, 2, 0, 0, 0, 0, 2, 2, 2, 0, 0, 1, 2, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 1, 1, 0, 1, 0, 1, 0, 2, 2, 2, 1, 2, 2, 0, 0, 0, 0, 1, 1, 2, 1, 2, 2, 1, 0, 1, 2, 2, 0, 2, 0, 0, 0, 2, 1, 2, 2, 1, 1, 1, 2, 2, 0, 1, 0, 2, 0, 2, 0, 0, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 2, 2, 2, 0, 2, 2, 2, 0, 1, 0, 2, 1, 1, 0, 2, 2, 2, 1, 0, 1, 1, 0, 2, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 1, 0, 0, 0, 0, 0, 1, 1, 2, 0, 2, 2, 0, 2, 1, 1, 1, 2, 0, 2, 0, 0, 2, 2, 1, 0, 0, 1, 1, 2, 2, 2, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 0, 1, 1, 2, 0, 0, 2, 0, 1, 0, 1, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 2, 0, 0, 0, 1, 1, 2, 0, 2, 2, 1, 0, 2, 2, 2, 1, 2, 0, 0, 2, 1, 2, 1, 2, 1, 1, 1, 0, 0, 0, 1, 2, 0, 2, 0, 1, 1, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 1, 2, 1, 2, 1, 0, 2, 2, 0, 0, 2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 2, 1, 1, 0, 2, 0, 1, 1, 1, 2, 2, 0, 2, 1, 2, 2, 2, 0, 0, 1, 2, 0, 1, 1, 0, 1, 2, 2, 2, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 0, 2, 1, 2, 0, 1 ] [2]: [75, 8, 44] Linear Code over GF(3) Puncturing of [1] at { 76 } last modified: 2008-11-04
Lb(75,8) = 43 is found by shortening of: Lb(76,9) = 43 is found by truncation of: Lb(81,9) = 48 BE Ub(75,8) = 45 follows by a one-step Griesmer bound from: Ub(29,7) = 15 is found by considering shortening 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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