Information on Result #698186
Linear OA(4942, 2419, F49, 19) (dual of [2419, 2377, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,6]) based on
- linear OA(4937, 2402, F49, 19) (dual of [2402, 2365, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(4925, 2402, F49, 13) (dual of [2402, 2377, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(495, 17, F49, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,49)), using
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), using
- Reed–Solomon code RS(44,49) [i]
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), 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(4942, 1775, F49, 2, 19) (dual of [(1775, 2), 3508, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4942, 1775, F49, 3, 19) (dual of [(1775, 3), 5283, 20]-NRT-code) | [i] | ||
| 3 | Digital (23, 42, 1775)-net over F49 | [i] | ||
| 4 | Linear OOA(4942, 1209, F49, 2, 19) (dual of [(1209, 2), 2376, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4942, 806, F49, 3, 19) (dual of [(806, 3), 2376, 20]-NRT-code) | [i] | ||