Information on Result #698279
Linear OA(4951, 2415, F49, 24) (dual of [2415, 2364, 25]-code), using construction X applied to Ce(23) ⊂ Ce(18) based on
- linear OA(4947, 2401, F49, 24) (dual of [2401, 2354, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(4937, 2401, F49, 19) (dual of [2401, 2364, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(494, 14, F49, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,49)), using
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), using
- Reed–Solomon code RS(45,49) [i]
- discarding factors / shortening the dual code based on linear OA(494, 49, F49, 4) (dual of [49, 45, 5]-code or 49-arc in PG(3,49)), 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(4951, 1299, F49, 2, 24) (dual of [(1299, 2), 2547, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4951, 1299, F49, 3, 24) (dual of [(1299, 3), 3846, 25]-NRT-code) | [i] | ||
| 3 | Digital (27, 51, 1299)-net over F49 | [i] | ||
| 4 | Linear OOA(4951, 1207, F49, 2, 24) (dual of [(1207, 2), 2363, 25]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4951, 805, F49, 3, 24) (dual of [(805, 3), 2364, 25]-NRT-code) | [i] | ||