Information on Result #676354
Linear OA(3158, 743, F3, 39) (dual of [743, 585, 40]-code), using construction X applied to C([0,19]) ⊂ C([0,18]) based on
- linear OA(3157, 730, F3, 39) (dual of [730, 573, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 312−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- linear OA(3145, 730, F3, 37) (dual of [730, 585, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 312−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(31, 13, F3, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3158, 743, F3, 2, 39) (dual of [(743, 2), 1328, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3158, 743, F3, 3, 39) (dual of [(743, 3), 2071, 40]-NRT-code) | [i] | ||
| 3 | Linear OOA(3158, 743, F3, 4, 39) (dual of [(743, 4), 2814, 40]-NRT-code) | [i] | ||
| 4 | Linear OOA(3158, 743, F3, 5, 39) (dual of [(743, 5), 3557, 40]-NRT-code) | [i] | ||
| 5 | Digital (119, 158, 743)-net over F3 | [i] | ||