Information on Result #698285
Linear OA(4939, 2415, F49, 18) (dual of [2415, 2376, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
- linear OA(4935, 2401, F49, 18) (dual of [2401, 2366, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(4925, 2401, F49, 13) (dual of [2401, 2376, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(4939, 1457, F49, 2, 18) (dual of [(1457, 2), 2875, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4939, 1457, F49, 3, 18) (dual of [(1457, 3), 4332, 19]-NRT-code) | [i] | ||
| 3 | Digital (21, 39, 1457)-net over F49 | [i] | ||
| 4 | Linear OOA(4939, 1207, F49, 2, 18) (dual of [(1207, 2), 2375, 19]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4939, 805, F49, 3, 18) (dual of [(805, 3), 2376, 19]-NRT-code) | [i] | ||