lower bound: | 39 |
upper bound: | 41 |
Construction of a linear code [69,9,39] over GF(3): [1]: [69, 9, 39] Linear Code over GF(3) Code found by Axel Kohnert and Johannes Zwanzger Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 2, 2, 0, 0, 1, 0, 2, 2, 2, 2, 0, 1, 0, 2, 0, 0, 2, 0, 1, 1, 1, 2, 1, 2, 0, 0, 2, 1, 0, 2, 1, 2, 1, 0, 1, 1, 0, 2, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 2, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 2, 2, 0 ] [ 0, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 0, 1, 2, 1, 0, 0, 1, 0, 2, 1, 2, 2, 2, 2, 0, 0, 1, 1, 1, 2, 0, 2, 0, 1, 2, 1, 0, 0, 1, 1, 0, 1, 2, 2, 0, 2, 1, 0, 2, 1, 2, 1, 0, 1, 2, 2, 0, 2, 0, 0, 2, 2, 1, 2, 0, 1 ] [ 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 1, 1, 2, 2, 0, 2, 1, 0, 2, 2, 1, 2, 2, 0, 0, 2, 1, 2, 0, 1, 0, 1, 0, 2, 1, 1, 2, 0, 0, 2, 2, 2, 2, 1, 2, 2, 2, 0, 0, 1, 2, 2, 0, 1, 1, 0, 1, 0, 2, 0, 1 ] [ 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 2, 0, 2, 1, 0, 2, 1, 2, 1, 0, 1, 1, 1, 2, 0, 2, 2, 2, 0, 0, 0, 2, 1, 1, 2, 1, 2, 2, 0, 1, 1, 1, 2, 0, 2, 2, 1, 2, 0, 2, 2, 1, 0, 2, 1, 0, 1, 1, 0, 1, 2, 2, 0, 2, 2, 2, 2, 2, 1 ] [ 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 1, 1, 1, 2, 0, 2, 1, 0, 2, 2, 1, 0, 0, 2, 2, 1, 2, 1, 0, 1, 1, 2, 2, 2, 1, 0, 0, 1, 0, 1, 2, 1, 1, 0, 0, 0, 1, 2, 2, 1, 0, 0, 2, 0, 2, 2, 2, 0, 1, 1, 0, 2, 1, 2 ] [ 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 0, 0, 1, 2, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 0, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 0, 0, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 2, 0, 2, 2, 2, 0, 1, 1, 0, 0, 2, 2, 0, 1, 1, 0, 1, 2, 0, 0, 0, 1, 2, 0, 0, 0, 1, 1, 2, 2, 2, 1, 0, 1, 0, 0, 2, 0, 1, 0, 1, 2, 1, 2, 2, 2, 0, 2, 2, 2, 2, 0, 2, 1, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 2, 1, 1, 0, 0, 1, 1, 2, 0, 0, 1, 2, 1, 0, 0, 0, 1, 1, 1, 2, 0, 0, 1, 1, 1, 2, 0, 2, 0, 0, 1, 2, 0, 1, 0, 1, 0, 1, 2, 1, 2, 1, 0, 0, 1, 1, 2, 1, 2, 1, 1, 2, 2, 0, 0, 1, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 2, 0, 1, 0, 0, 1, 1, 2, 2, 0, 2, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 2, 0, 0, 2, 0, 2, 0, 2, 1, 0, 2, 1, 2, 0, 2, 0, 1, 2, 2, 2, 1, 1, 0, 2, 2, 0, 2, 1, 2, 2, 0 ] last modified: 2008-10-21
Lb(69,9) = 38 is found by truncation of: Lb(70,9) = 39 GB4 Ub(69,9) = 41 is found by considering shortening to: Ub(67,7) = 41 BKn
GB4: T. A. Gulliver & V. K. Bhargava, New good rate $(m-1)/pm$ ternary and quaternary cyclic codes, Des. Codes Cryptogr. 7 (1996) 223-233.
Notes
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