lower bound: | 122 |
upper bound: | 126 |
Construction of a linear code [195,8,122] over GF(3): [1]: [196, 8, 123] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 1, 0, 0, 1, 2, 0, 2, 2, 1, 0, 2, 1, 2, 0, 2, 2, 0, 1, 2, 1, 1, 1, 2, 1, 0, 1, 2, 2, 2, 0, 1, 0, 2, 1, 0, 2, 2, 0, 0, 0, 2, 1, 0, 1, 0, 1, 0, 2, 2, 1, 2, 0, 1, 2, 2, 0, 2, 1, 0, 2, 0, 2, 2, 1, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 1, 1, 0, 0, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2, 1, 2, 0, 0, 2, 2, 2, 1, 0, 1, 1, 0, 2, 2, 2, 2, 1, 2, 2, 1, 0, 0, 0, 0, 1, 0, 2, 0, 0, 2, 2, 0, 2, 2, 1, 2, 0, 0, 1, 2, 0, 0, 1, 0, 2, 2, 2, 0, 2, 0, 1, 1, 2, 2, 0, 1, 0, 2, 2, 0, 2, 0, 1, 0, 2, 0, 0, 0, 2, 2, 1, 1, 0, 0, 1, 1, 2, 1, 0, 1, 0, 2, 2, 2, 1, 1, 0, 1, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 1, 1, 2, 1, 1, 1, 0, 2, 1, 2, 2, 1, 0, 0, 2, 2, 2, 2, 1, 0, 0, 2, 1, 2, 2, 2, 2, 1, 2, 0, 2, 0, 1, 2, 2, 0, 1, 2, 2, 1, 1, 0, 0, 1, 0, 1, 1, 0, 2, 0, 0, 0, 0, 1, 1, 0, 0, 2, 1, 1, 2, 0, 2, 2, 0, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 2, 2, 2, 0, 1, 0, 2, 0, 1, 0, 2, 1, 2, 0, 0, 2, 1, 2, 1, 1, 0, 2, 2, 1, 2, 1, 2, 0, 2, 0, 0, 1, 0, 2, 1, 2, 2, 1, 0, 1, 1, 2, 0, 2, 2, 2, 0, 0, 1, 2, 2, 1, 1, 1, 0, 2, 2, 1, 2, 1, 0, 1, 2, 0, 1, 1, 2, 2, 2, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 2, 2, 0, 2, 2, 1, 0, 2, 1, 0, 2 ] [ 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 2, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 2, 2, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 2, 1, 1, 1, 2, 0, 2, 0, 0, 1, 2, 2, 2, 0, 0, 2, 1, 0, 1, 0, 2, 1, 1, 0, 2, 2, 1, 2, 0, 0, 2, 1, 0, 1, 0, 0, 1, 2, 2, 0, 0, 0, 0, 2, 1, 0, 2, 2, 2, 2, 1, 2, 1, 0, 2, 0, 2, 2, 0, 0, 1, 0, 0, 2, 0, 1, 2, 2, 2, 0, 1, 2, 0, 1, 1, 2, 0, 1, 1, 1, 2, 2, 2, 1, 0, 2, 0, 0, 1, 0, 0, 1, 0, 2, 2, 0, 0, 0, 1, 0, 0, 0, 2, 2, 1, 2, 0, 0, 2, 0, 1, 0, 1, 2, 0, 0, 0, 1, 0, 0, 1, 2, 2, 1, 1, 1, 0, 1, 0, 2, 2, 2, 2, 0, 0, 2, 2, 1, 1, 1, 2, 0, 1, 2, 2, 1, 2, 2, 2, 0, 2, 1, 0, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 1, 2, 1, 2, 0, 2, 2, 0, 1, 1, 1, 0, 2, 2, 1, 1, 1, 0, 2, 2, 1, 1, 2, 0, 0, 0, 1, 2, 1, 1, 1, 1, 2, 1, 2, 0, 0, 2, 1, 2, 1, 2, 0, 2, 2, 0, 1, 2, 2, 0, 1, 0, 0, 1, 0, 2, 0, 0, 1, 2, 0, 0, 2, 0, 2, 2, 0, 0, 2, 1, 2, 1, 0, 1, 0, 0, 0, 1, 0, 2, 1, 0, 0, 2, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 1, 2, 1, 1, 0, 2, 2, 0, 1, 1, 2, 2, 2, 0, 1, 2, 0, 2, 1, 0, 2, 1, 2, 2, 0, 1, 1, 0, 0, 2, 1, 2, 1, 0, 1, 1, 2, 2, 1, 2, 2, 0, 1, 0, 2, 1, 1, 0, 2, 2, 1, 0, 2, 0, 2, 2, 1, 1, 0, 1, 2, 2, 2, 1, 1, 2, 0, 1, 2, 0, 2, 0, 2, 1 ] [ 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 1, 2, 1, 1, 2, 1, 2, 2, 2, 2, 0, 2, 0, 2, 1, 2, 0, 2, 2, 1, 0, 1, 2, 1, 0, 0, 0, 1, 2, 0, 1, 1, 1, 2, 0, 0, 2, 2, 1, 0, 1, 1, 0, 2, 0, 2, 2, 2, 1, 2, 1, 0, 0, 2, 0, 0, 1, 0, 2, 0, 1, 0, 2, 1, 2, 1, 0, 1, 1, 2, 0, 1, 0, 0, 0, 2, 2, 2, 0, 2, 0, 0, 2, 2, 1, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 1, 2, 0, 1, 2, 1, 1, 2, 2, 1, 1, 0, 2, 0, 1, 0, 2, 0, 0, 0, 1, 1, 0, 0, 0, 2, 2, 2, 1, 0, 0, 2, 0, 1, 2, 0, 1, 2, 2, 1, 0, 0, 1, 0, 1, 2, 1, 2, 0, 0, 0, 2, 2, 0, 2, 0, 2, 1, 2, 0, 1, 2, 0, 1, 2, 0, 1, 2, 1, 2, 1, 2, 2, 1, 0, 2, 2, 2, 0, 1, 0, 2, 1, 0, 2, 1, 1, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 0, 1, 2, 0, 0, 1, 1, 0, 1, 1, 2, 2, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 1, 0, 2, 0, 2, 2, 0, 1, 0, 1, 2, 2, 2, 1, 2, 1, 2, 0, 2, 1, 2, 2, 0, 1, 2, 0, 2, 2, 0, 0, 1, 1, 0, 2, 1, 1, 2, 2, 0, 2, 2, 1, 2, 1, 2, 0, 1, 1, 2, 2, 0, 2, 1, 0, 0, 0, 1, 1, 2, 2, 0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 2, 1, 1, 0, 0, 1, 2, 0, 1, 1, 2, 1, 1, 1, 2, 2, 0, 0, 1, 2, 1, 0, 2, 0, 2, 2, 1, 0, 1, 0, 0, 0, 2, 2, 1, 0, 2, 2, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 1, 0, 0, 1, 1, 0, 1, 2, 1, 0, 1, 2, 0, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 1, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0, 2, 1, 2, 1, 0, 0, 2, 1, 1, 2, 2, 0, 2, 1, 1, 2, 2, 1, 0, 0, 2, 1, 2, 1, 0, 0, 0, 1, 1, 0, 2, 1, 2, 2, 2, 0, 2, 2, 1, 1, 0, 2, 0, 2, 1, 2, 1, 1, 1, 1, 2, 0, 0, 1, 0, 0, 2, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0, 2, 2, 2, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 2, 2, 1, 2, 0, 0, 1, 0, 2, 2, 0, 1, 2, 2, 2, 2, 1, 0, 0, 2, 1, 1, 2, 2, 2, 2, 1, 2, 0, 1, 1, 1, 2, 0, 0, 1, 2, 0, 2, 1, 2, 1, 2, 2, 1, 0, 1, 1, 0, 0, 2, 0, 1, 1, 2, 1, 0, 1, 1, 0, 1, 2, 2, 1, 2, 2, 2, 1, 0, 2, 1, 1, 1, 1, 1, 2, 0, 2, 0, 0, 0, 2, 1, 2, 0, 2, 2, 2, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 2, 0, 2, 1, 2, 0, 0, 1, 2, 0, 2, 1, 2, 1, 2, 0, 0, 2, 1, 2, 1, 1, 0, 1, 1, 2, 1, 2, 0, 1, 1, 1, 0, 0, 2, 0, 1, 1, 0, 0, 1, 2, 2, 1, 1, 2, 2, 1, 2, 2, 0, 2, 0, 1, 0, 2, 1, 0, 1, 1, 0, 1, 0, 0, 1, 2, 0, 0, 1, 2, 0, 1, 0, 0, 0, 2, 1, 0, 0, 2, 2, 2, 0, 1, 0, 2, 0, 0, 2, 2, 0, 1, 0, 1, 0, 0, 2, 0, 1, 1, 2, 0, 0, 1, 2, 2, 1, 1, 0, 1, 2, 2, 1, 2, 1, 0, 1, 0, 2, 2, 1, 0, 2, 0, 1, 2, 0, 2, 2, 1, 1, 0, 2, 2, 1, 1, 2, 0, 2, 0, 2, 1, 2, 1, 1, 0, 2, 1, 2, 2, 2, 2, 1, 2, 0, 1, 1, 1, 1, 2, 0, 2, 1, 0, 0, 2, 2, 0, 0, 2, 0, 2, 2, 2 ] [2]: [195, 8, 122] Linear Code over GF(3) Puncturing of [1] at { 196 } last modified: 2008-11-04
Lb(195,8) = 121 is found by truncation of: Lb(200,8) = 126 BKW Ub(195,8) = 126 follows by a one-step Griesmer bound from: Ub(68,7) = 42 follows by a one-step Griesmer bound from: Ub(25,6) = 14 is found by considering shortening to: Ub(23,4) = 14 is found by considering truncation to: Ub(21,4) = 12 HN
HN: R. Hill & D.E. Newton, Optimal ternary linear codes, Des. Codes Cryptogr. 2 (1992), 137-157.
Notes
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