lower bound: | 46 |
upper bound: | 48 |
Construction of a linear code [78,8,46] 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 ] [2]: [79, 9, 46] Linear Code over GF(3) Puncturing of [1] at { 80 .. 81 } [3]: [78, 8, 46] Linear Code over GF(3) Shortening of [2] at { 79 } last modified: 2001-12-17
Lb(78,8) = 46 is found by shortening of: Lb(79,9) = 46 is found by truncation of: Lb(81,9) = 48 BE Ub(78,8) = 48 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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