Information on Result #698283
Linear OA(4943, 2415, F49, 20) (dual of [2415, 2372, 21]-code), using construction X applied to Ce(19) ⊂ Ce(14) 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(4929, 2401, F49, 15) (dual of [2401, 2372, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(4943, 1374, F49, 2, 20) (dual of [(1374, 2), 2705, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4943, 1374, F49, 3, 20) (dual of [(1374, 3), 4079, 21]-NRT-code) | [i] | ||
| 3 | Digital (23, 43, 1374)-net over F49 | [i] | ||
| 4 | Linear OOA(4943, 1207, F49, 2, 20) (dual of [(1207, 2), 2371, 21]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4943, 805, F49, 3, 20) (dual of [(805, 3), 2372, 21]-NRT-code) | [i] | ||