lower bound: | 72 |
upper bound: | 72 |
Construction of a linear code [114,7,72] over GF(3): [1]: [112, 7, 72] Linear Code over GF(3) Construction from a stored generator matrix: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 0, 0, 0, 0, 2, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 1, 2, 2, 2, 1, 0, 0, 0, 0, 1, 1, 2, 2, 2, 0, 0, 0, 0, 2, 2, 0, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 0, 1, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 1, 2, 1, 1, 2, 1, 2, 2, 2, 1, 1, 1 ] [ 0, 1, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 0, 2, 0, 1, 0, 0, 2, 2, 2, 2, 2, 1, 2, 0, 2, 1, 0, 0, 1, 2, 2, 1, 0, 1, 1, 1, 1, 2, 1, 0, 2, 2, 0, 1, 1, 2, 0, 2, 2, 0, 0, 1, 1, 0, 1, 2, 2, 2, 1, 2, 1, 0, 2, 2, 2, 1, 2, 0, 2, 2, 2, 2, 0, 0, 0, 2, 2, 1, 0, 2, 0, 1, 1, 0, 0, 2, 2, 0, 2, 0, 1, 0, 1, 2, 2, 0, 2, 1, 2, 0, 0, 0, 2, 1 ] [ 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 1, 1, 2, 1, 0, 1, 0, 0, 2, 0, 0, 2, 1, 0, 2, 0, 0, 1, 2, 2, 2, 2, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 2, 2, 2, 1, 2, 0, 1, 2, 2, 1, 0, 1, 0, 1, 1, 1, 2, 0, 2, 0, 0, 2, 2, 1, 0, 1, 0, 2, 2, 1, 0, 2, 1, 2, 2, 2, 1, 0, 2, 2, 0, 0, 0, 1, 2, 1, 2, 2, 2, 0, 0, 1, 1, 0, 1, 2, 1, 1, 1, 0, 0, 1, 0, 1 ] [ 0, 0, 0, 0, 0, 1, 0, 1, 2, 0, 0, 0, 0, 2, 0, 0, 1, 0, 2, 2, 1, 1, 2, 2, 2, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 0, 2, 1, 2, 2, 2, 0, 0, 1, 1, 1, 1, 2, 2, 2, 1, 0, 2, 0, 1, 2, 2, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 2, 0, 2, 2, 0, 2, 1, 2, 0, 0, 2, 2, 2, 1, 0, 0, 2, 2, 1, 0, 0, 2, 2, 2, 2, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 2, 1, 2, 1, 1 ] [ 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 1, 0, 2, 1, 0, 0, 1, 2, 1, 1, 0, 2, 0, 0, 2, 2, 2, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 2, 1, 0, 2, 0, 2, 0, 2, 2, 1, 1, 2, 0, 0, 1, 1, 2, 1, 0, 1, 1, 1, 2, 1, 0, 2, 2, 2, 1, 2, 2, 0, 2, 1, 0, 2, 2, 0, 2, 1, 0, 2, 1, 1, 1, 2, 2, 1, 2, 0, 1, 2, 1, 1, 2, 2, 1, 1, 2, 2, 0 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 1, 1, 2, 1, 0, 2, 0, 0, 2, 1, 2, 0, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 2, 0, 2, 1, 0, 2, 1, 0, 1, 0, 1, 2, 1, 2, 1, 2, 0, 0, 2, 2, 2, 2, 1, 0, 1, 0, 0, 1, 1, 1, 0, 0, 2, 1, 0, 2, 0, 1, 0, 0, 0, 2, 2, 2, 2, 0, 0, 0, 0, 2, 1, 0, 2, 1, 1, 2, 2, 0, 2, 1, 2, 2, 2, 1, 1, 0, 2, 2, 1 ] [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 0, 1, 2, 1, 1, 2, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 2, 0, 0, 0, 0, 2, 0, 1, 1, 2, 0, 0, 1, 0, 0, 1, 0, 1, 2, 0, 0, 0, 1, 1, 1, 1, 0, 1, 2, 0, 2, 2, 1, 0, 1, 2, 2, 2, 0, 1, 1, 2, 0, 2, 0, 1, 0, 1, 2, 2, 0, 2, 0, 2, 2, 1, 0, 2, 2, 1, 2, 2, 1, 1, 1, 2, 1, 2, 0, 2, 1, 1, 0, 0, 2, 0, 1, 1, 1, 2, 1, 1 ] [2]: [114, 7, 72] Linear Code over GF(3) PadCode [1] by 2 last modified: 2001-12-17
Lb(114,7) = 72 is found by lengthening of: Lb(112,7) = 72 EB1 Ub(114,7) = 72 follows by a one-step Griesmer bound from: Ub(41,6) = 24 is found by considering shortening 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
|