lower bound: | 78 |
upper bound: | 79 |
Construction of a linear code [123,7,78] over GF(3): [1]: [123, 7, 78] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 1, 1, 2, 2, 1, 0, 1, 1, 1, 1, 2, 0, 0, 1, 1, 2, 1, 2, 1, 0, 0, 0, 2, 0, 1, 2, 1, 1, 0, 0, 1, 0, 0, 1, 1, 1, 0, 2, 2, 0, 2, 1, 1, 0, 2, 0, 1, 2, 2, 0, 1, 2, 0, 2, 0, 2, 2, 0, 1, 2, 2, 1, 2, 0, 0, 1, 1, 1, 1, 1, 1, 2, 0, 2, 2, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 0, 2, 1, 2, 2, 2, 1, 1, 1, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 0, 1, 1, 1, 0 ] [ 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 1, 1, 1, 0, 0, 2, 0, 2, 1, 1, 1, 1, 2, 2, 1, 1, 0, 0, 0, 1, 2, 2, 2, 0, 1, 2, 0, 0, 2, 0, 2, 2, 2, 1, 0, 0, 2, 2, 2, 1, 0, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 1, 0, 0, 2, 2, 2, 1, 0, 2, 1, 2, 1, 0, 2, 2, 2, 1, 0, 2, 2, 2, 2, 0, 0, 0, 0, 0, 1, 1, 0, 2, 0, 2, 1, 1, 2, 0, 2, 0, 0, 0, 2, 0, 2, 2, 0, 2, 2, 2, 0, 0, 1, 0, 2, 1 ] [ 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 2, 1, 1, 2, 0, 2, 0, 1, 0, 0, 0, 0, 2, 0, 2, 2, 0, 2, 0, 2, 1, 1, 2, 1, 2, 2, 0, 2, 2, 0, 2, 0, 0, 2, 2, 2, 2, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 2, 2, 0, 0, 1, 0, 2, 2, 1, 2, 1, 0, 0, 2, 0, 2, 0, 2, 1, 0, 1, 1, 2, 0, 2, 1, 2, 2, 0, 2, 1, 2, 0, 1, 2, 1, 1, 2, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 1, 1, 2, 1, 0, 2, 0, 1, 1, 2, 1, 1, 2, 0, 1, 1, 0, 0, 1, 0, 0, 2, 2, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 2, 1, 1, 0, 1, 2, 1, 1, 2, 1, 0, 2, 2, 1, 2, 1, 0, 2, 0, 0, 2, 2, 1, 0, 0, 0, 2, 2, 0, 1, 1, 2, 1, 1, 2, 1, 0, 2, 1, 1, 1, 2, 0, 2, 1, 0, 1, 1, 2, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 1, 2, 0, 2 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 2, 2, 0, 1, 1, 1, 1, 0, 1, 2, 0, 2, 1, 0, 2, 1, 2, 0, 0, 1, 1, 2, 1, 2, 2, 0, 2, 0, 2, 2, 1, 0, 0, 1, 0, 1, 1, 2, 0, 0, 0, 2, 2, 1, 0, 2, 1, 1, 2, 0, 0, 1, 1, 1, 1, 2, 1, 2, 2, 0, 1, 2, 0, 1, 0, 2, 0, 2, 0, 2, 1, 0, 1, 0, 1, 2, 2, 2, 0, 0, 2, 2, 2, 2, 1, 1, 0, 1, 2, 0, 1, 2, 2, 1, 2, 2, 1, 0, 0, 1, 0, 0, 2, 1, 2, 0, 1, 2, 0, 0, 0, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 0, 0, 0, 1, 0, 1, 2, 1, 1, 2, 0, 2, 2, 2, 0, 1, 1, 2, 2, 2, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 2, 1, 0, 1, 2, 0, 2, 1, 2, 1, 2, 1, 0, 2, 0, 2, 2, 0, 2, 2, 0, 1, 2, 0, 2, 0, 2, 0, 0, 2, 2, 1, 1, 0, 0, 0, 2, 0, 2, 1, 0, 0, 2, 2, 2, 1, 2, 2, 1, 0, 1, 2, 2, 0, 2, 2, 2, 1, 0, 2, 2, 1, 1, 0, 2, 1, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 2, 1, 1, 2, 0, 1, 1, 1, 1, 2, 0, 1, 2, 1, 2, 2, 0, 1, 2, 1, 1, 1, 0, 0, 2, 2, 2, 0, 0, 1, 0, 0, 1, 1, 2, 0, 2, 0, 0, 2, 2, 2, 0, 0, 2, 2, 1, 2, 0, 0, 1, 0, 0, 1, 2, 1, 0, 0, 0, 2, 2, 2, 1, 2, 1, 1, 2, 0, 2, 1, 2, 0, 1, 0, 2, 2, 2, 2, 1, 0, 1, 1, 2, 1, 0, 2, 2, 2, 1, 0, 0, 2, 0, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 1, 0, 1, 2, 2 ] last modified: 2007-08-03
Lb(123,7) = 77 is found by truncation of: Lb(127,7) = 81 GW2 Ub(123,7) = 79 follows by a one-step Griesmer bound from: Ub(43,6) = 26 is found by considering shortening to: Ub(42,5) = 26 is found by considering truncation to: Ub(40,5) = 24 vE1
vE1: M. van Eupen, Some new results for ternary linear codes of dimension $5$ and $6$, IEEE Trans. Inform. Theory 41 (1995) 2048-2051.
Notes
|