lower bound: | 126 |
upper bound: | 127 |
Construction of a linear code [195,7,126] over GF(3): [1]: [194, 7, 126] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 2, 0, 2, 0, 0, 1, 0, 2, 2, 2, 1, 1, 0, 0, 2, 0, 1, 2, 2, 0, 2, 2, 0, 0, 0, 2, 2, 1, 2, 1, 2, 2, 0, 2, 0, 0, 1, 2, 0, 2, 1, 2, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 2, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2, 1, 2, 1, 0, 2, 1, 1, 0, 1, 2, 0, 2, 2, 1, 2, 1, 2, 1, 2, 0, 1, 2, 1, 2, 1, 0, 0, 2, 0, 2, 2, 1, 1, 0, 0, 1, 0, 1, 2, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 2, 1, 1, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 2, 1, 0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 1, 0, 2, 1, 1, 0, 1, 2, 2, 0, 1, 1, 0, 1, 0, 0, 2, 2, 0, 0, 2, 1, 1, 0, 2, 1, 2, 2 ] [ 0, 1, 0, 0, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 0, 0, 1, 1, 1, 2, 2, 0, 2, 2, 0, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 2, 0, 2, 0, 1, 2, 1, 2, 2, 0, 2, 2, 0, 1, 2, 2, 0, 2, 2, 2, 0, 2, 1, 0, 0, 1, 2, 2, 2, 2, 0, 2, 1, 0, 1, 1, 1, 1, 1, 2, 0, 2, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 0, 1, 2, 0, 2, 1, 2, 2, 1, 1, 2, 2, 0, 2, 2, 1, 1, 2, 2, 0, 0, 1, 1, 1, 2, 1, 1, 2, 2, 0, 2, 1, 0, 1, 0, 2, 0, 2, 0, 0, 1, 2, 1, 2, 2, 2, 0, 0, 2, 2, 1, 0, 1, 1, 0, 1, 0, 2, 2, 0, 2, 2, 0, 0, 1, 0, 2, 1, 1, 0, 1, 2, 0, 0, 1, 1, 0, 0, 0, 2, 0, 2, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 1, 2, 1, 0, 2, 2 ] [ 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 0, 0, 2, 1, 1, 1, 1, 0, 1, 0, 2, 0, 0, 1, 0, 1, 2, 1, 1, 1, 2, 0, 2, 1, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 0, 2, 1, 0, 1, 1, 0, 1, 2, 2, 1, 0, 1, 0, 2, 1, 0, 1, 1, 0, 2, 0, 2, 0, 1, 2, 2, 2, 2, 2, 2, 0, 2, 2, 0, 2, 2, 0, 2, 1, 1, 1, 2, 2, 1, 1, 0, 2, 0, 0, 0, 2, 0, 2, 1, 1, 2, 2, 0, 1, 1, 2, 1, 2, 0, 0, 2, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 1, 2, 2, 0, 0, 1, 1, 2, 1, 0, 0, 2, 1, 2, 1, 2, 2, 2, 0, 2, 0, 0, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 0, 2, 2, 2, 0, 0, 2, 1, 2, 0, 1, 1, 1, 1, 0, 2, 1, 0, 0, 1, 2, 1, 0, 1, 2, 0, 0, 2, 1, 1 ] [ 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 2, 2, 2, 0, 2, 0, 0, 0, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 1, 1, 2, 2, 0, 2, 0, 2, 2, 2, 0, 0, 2, 2, 1, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 1, 1, 2, 0, 1, 2, 1, 2, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 2, 0, 1, 2, 0, 1, 1, 2, 1, 2, 2, 1, 0, 1, 1, 0, 1, 1, 0, 1, 2, 0, 2, 2, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 2, 2, 1, 1, 0, 0, 0, 2, 2, 0, 0, 1, 1, 0, 2, 1, 2, 2, 2, 2, 1, 1, 0, 0, 2, 0, 1, 2, 1, 1, 2, 2, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 2, 0, 2, 1, 2, 1, 1, 1, 2, 0, 2, 1, 2, 2, 0, 0, 2, 1, 1, 1, 2, 2, 2, 1, 0, 1, 2, 0, 2, 0, 0 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 2, 1, 2, 0, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 2, 0, 1, 0, 2, 2, 0, 2, 2, 2, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 2, 2, 2, 2, 1, 2, 0, 1, 2, 0, 1, 2, 2, 1, 2, 2, 0, 2, 1, 2, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 2, 2, 0, 0, 1, 2, 1, 0, 0, 1, 2, 1, 1, 0, 1, 1, 2, 0, 2, 0, 1, 2, 1, 1, 0, 0, 1, 1, 0, 0, 2, 0, 1, 1, 1, 1, 2, 0, 1, 1, 2, 0, 2, 2, 2, 2, 0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 0, 1, 0, 2, 0, 1, 2, 2, 1, 0, 0, 0, 2, 2, 0, 2, 0, 1, 2, 1, 2, 1, 2, 0, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 1, 2, 2, 2, 0, 1, 1, 2, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 2, 2, 2, 0, 2, 2, 0, 2, 0, 2, 0, 2, 0, 2, 1, 0, 1, 2, 2, 2, 2, 2, 0, 2, 1, 0, 1, 2, 2, 1, 0, 2, 2, 1, 0, 0, 2, 1, 2, 1, 2, 1, 0, 2, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 2, 0, 2, 1, 0, 2, 2, 2, 1, 2, 0, 0, 1, 1, 1, 1, 2, 2, 0, 2, 2, 2, 2, 1, 2, 1, 2, 2, 0, 0, 0, 1, 2, 1, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 2, 0, 1, 1, 0, 1, 2, 0, 1, 1, 1, 1, 2, 2, 0, 1, 1, 0, 2, 1, 2, 2, 0, 0, 2, 1, 0, 2, 2, 2, 1, 2, 1, 1, 2, 0, 1, 1, 1, 2, 2, 0, 0, 1, 2, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 2, 1, 2, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 2, 1, 0, 0, 1, 1, 2, 0, 0, 0, 2, 1, 2, 1, 0, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 0, 1, 2, 2, 2, 1, 2, 1, 1, 2, 1, 1, 0, 0, 1, 2, 2, 0, 2, 2, 1, 1, 2, 1, 1, 1, 0, 2, 0, 1, 1, 2, 2, 0, 0, 2, 0, 1, 1, 1, 0, 0, 0, 1, 2, 2, 2, 0, 0, 0, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 0, 2, 2, 1, 0, 2, 2, 0, 2, 1, 2, 1, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 1, 1, 0, 0, 2, 2, 1, 2, 2, 2, 1, 2, 1, 2, 1, 0, 1, 1, 2, 2, 0, 1, 2, 0, 0, 2, 1, 2, 0, 1, 2, 2, 1, 1, 1, 0, 2, 2, 1, 0, 1, 1, 2, 2, 1, 1, 0, 2, 0, 2, 1, 2, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 2, 1, 0, 0, 0, 2, 0, 1, 2, 2, 2, 1, 1 ] [2]: [195, 7, 126] Linear Code over GF(3) ExtendCode [1] by 1 last modified: 2008-12-29
Lb(195,7) = 125 is found by truncation of: Lb(196,7) = 126 GO Ub(195,7) = 127 follows by a one-step Griesmer bound from: Ub(67,6) = 42 follows by a one-step Griesmer bound from: Ub(24,5) = 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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