Information on Result #676374
Linear OA(374, 743, F3, 17) (dual of [743, 669, 18]-code), using construction X applied to C([0,9]) ⊂ C([0,7]) based on
- linear OA(373, 730, F3, 19) (dual of [730, 657, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 312−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(361, 730, F3, 15) (dual of [730, 669, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 730 | 312−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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(374, 661, F3, 2, 17) (dual of [(661, 2), 1248, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(374, 661, F3, 3, 17) (dual of [(661, 3), 1909, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(374, 661, F3, 4, 17) (dual of [(661, 4), 2570, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(374, 661, F3, 5, 17) (dual of [(661, 5), 3231, 18]-NRT-code) | [i] | ||
| 5 | Digital (57, 74, 661)-net over F3 | [i] | ||