lower bound: | 60 |
upper bound: | 64 |
Construction of a linear code [105,10,60] over GF(3): [1]: [105, 10, 60] Linear Code over GF(3) Code found by Axel Kohnert Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 1, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 1, 1, 1, 2, 0, 1, 2, 1, 0, 2, 0, 2, 1, 0, 1, 1, 1, 0, 1, 2, 2, 1, 0, 0, 2, 0, 2, 1, 0, 2, 1, 0, 0, 2, 0, 2, 1, 2, 2, 0, 2, 0, 0, 2, 2, 1, 1, 2, 1, 1, 0, 2, 2, 1, 2, 0, 1, 2, 1, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 2, 0, 0 ] [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 1, 0, 2, 2, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 0, 2, 2, 0, 2, 1, 2, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 0, 0, 2, 1, 0, 2, 0, 1, 0, 0, 2, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 1, 2, 2, 0, 0, 0, 0, 0, 2, 2, 2, 0, 0, 0, 1, 0, 2, 0, 1, 0, 1, 2, 2, 0, 0, 0, 0 ] [ 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 2, 1, 1, 1, 2, 2, 0, 2, 0, 1, 1, 2, 1, 2, 2, 2, 1, 2, 0, 0, 2, 1, 2, 1, 2, 0, 0, 1, 2, 1, 0, 2, 2, 1, 0, 1, 2, 1, 0, 2, 0, 0, 2, 2, 0, 0, 0, 0, 2, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 2, 0, 2, 0, 2, 0, 1, 1, 0, 0, 2, 1, 1, 2, 1, 2, 2, 1, 0, 1, 0, 1, 2, 2, 1, 2, 2, 1, 2, 2 ] [ 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 1, 1, 2, 2, 1, 2, 0, 0, 2, 1, 0, 0, 0, 1, 0, 2, 2, 1, 0, 0, 0, 0, 1, 2, 2, 0, 0, 2, 0, 2, 1, 2, 1, 1, 0, 1, 2, 2, 2, 1, 0, 2, 1, 0, 2, 0, 0, 1, 2, 0, 2, 0, 0, 0, 1, 2, 1, 0, 2, 1, 0, 0, 0, 1, 0, 2, 2, 1, 1, 0, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 2, 1, 2, 0, 1, 1, 0, 0, 1, 0, 2, 1, 0, 2 ] [ 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 2, 1, 2, 2, 1, 0, 0, 2, 1, 2, 2, 2, 1, 0, 2, 1, 2, 2, 0, 1, 2, 1, 2, 1, 0, 1, 0, 2, 2, 2, 2, 2, 2, 2, 1, 0, 1, 1, 2, 1, 0, 0, 1, 2, 0, 0, 0, 1, 2, 1, 2, 0, 0, 2, 0, 2, 2, 0, 2, 1, 1, 1, 0, 0, 2, 0, 2, 1, 1, 0, 1, 1, 1, 2, 1, 0, 1, 0, 0, 0, 1, 2, 2, 2, 0, 2, 1, 1, 2, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 2, 0, 0, 2, 0, 1, 2, 0, 1, 0, 0, 1, 0, 0, 1, 0, 1, 2, 2, 1, 1, 1, 0, 2, 1, 0, 2, 1, 2, 0, 0, 1, 2, 1, 2, 0, 1, 0, 0, 2, 1, 0, 0, 1, 0, 2, 2, 2, 2, 2, 0, 0, 0, 1, 2, 0, 1, 2, 1, 2, 1, 1, 0, 2, 2, 1, 2, 2, 0, 0, 2, 2, 0, 2, 1, 1, 0, 1, 1, 0, 2, 0, 2, 1, 1, 1, 2, 1, 0, 1, 0, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 1, 2, 0, 2, 2, 0, 1, 2, 0, 2, 0, 2, 0, 2, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 0, 1, 1, 0, 2, 1, 2, 2, 2, 1, 0, 0, 0, 2, 2, 0, 0, 2, 1, 1, 1, 2, 1, 2, 1, 1, 2, 2, 1, 0, 0, 2, 2, 1, 0, 1, 1, 2, 1, 1, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 0, 2, 1, 1, 2, 2, 2, 2, 0, 2, 0, 1, 2, 1, 0, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 2, 0, 0, 1, 2, 2, 1, 1, 0, 1, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 2, 0, 1, 1, 2, 0, 0, 2, 1, 1, 2, 2, 2, 2, 1, 0, 1, 0, 1, 2, 0, 0, 1, 1, 0, 1, 0, 2, 0, 2, 0, 2, 1, 2, 2, 2, 0, 0, 1, 1, 1, 2, 0, 1, 1, 2, 2, 0, 1, 1, 0, 0, 0, 1, 2, 1, 1, 0, 1, 2, 2, 1, 1, 2, 2, 2, 2, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 2, 0, 2, 0, 0, 2, 2, 0, 2, 1, 0, 2, 0, 0, 1, 2, 2, 0, 0, 1, 1, 1, 2, 0, 0, 2, 2, 2, 0, 0, 0, 2, 1, 0, 1, 2, 1, 2, 2, 2, 2, 1, 1, 1, 1, 0, 2, 2, 1, 0, 2, 0, 1, 1, 1, 2, 2, 2, 2, 1, 2, 0, 0, 0, 0, 1, 0, 2, 2, 2, 0, 2, 2, 1, 2, 1, 0, 1, 0, 2, 0, 1, 1, 0, 2, 1, 2, 2, 0, 0, 1, 1, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 1, 0, 0, 2, 2, 2, 2, 0, 1, 2, 1, 2, 1, 2, 2, 1, 1, 0, 2, 0, 0, 1, 0, 2, 2, 1, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 0, 1, 1, 0, 2, 2, 0, 0, 0, 0, 0, 2, 1, 2, 1, 2, 2, 0, 0, 1, 2, 1, 2, 2, 0, 0, 0, 0, 1, 0, 2, 0, 0, 1, 1, 2, 2, 2, 1, 1, 1, 2, 0, 2, 2, 0, 0, 1, 1, 1, 1, 1, 2, 1, 2 ] last modified: 2010-11-13
Lb(105,10) = 58 is found by truncation of: Lb(106,10) = 59 MTS Ub(105,10) = 64 follows by a one-step Griesmer bound from: Ub(40,9) = 21 follows by a one-step Griesmer bound from: Ub(18,8) = 7 is found by considering shortening to: Ub(16,6) = 7 vE2
vE2: M. van Eupen, Four nonexistence results for ternary linear codes, IEEE Trans. Inform. Theory 41 (1995) 800-805.
Notes
|