Information on Result #698296
Linear OA(4944, 2418, F49, 20) (dual of [2418, 2374, 21]-code), using construction X applied to Ce(19) ⊂ Ce(13) based on
- linear OA(4939, 2401, F49, 20) (dual of [2401, 2362, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(4927, 2401, F49, 14) (dual of [2401, 2374, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(4944, 1708, F49, 2, 20) (dual of [(1708, 2), 3372, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4944, 1708, F49, 3, 20) (dual of [(1708, 3), 5080, 21]-NRT-code) | [i] | ||
| 3 | Digital (24, 44, 1708)-net over F49 | [i] | ||
| 4 | Linear OOA(4944, 1209, F49, 2, 20) (dual of [(1209, 2), 2374, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4944, 806, F49, 3, 20) (dual of [(806, 3), 2374, 21]-NRT-code) | [i] | ||