Information on Result #698286
Linear OA(4937, 2415, F49, 17) (dual of [2415, 2378, 18]-code), using construction X applied to Ce(16) ⊂ Ce(11) based on
- linear OA(4933, 2401, F49, 17) (dual of [2401, 2368, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(4937, 1517, F49, 2, 17) (dual of [(1517, 2), 2997, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4937, 1517, F49, 3, 17) (dual of [(1517, 3), 4514, 18]-NRT-code) | [i] | ||
| 3 | Digital (20, 37, 1517)-net over F49 | [i] | ||
| 4 | Linear OOA(4937, 1207, F49, 2, 17) (dual of [(1207, 2), 2377, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4937, 805, F49, 3, 17) (dual of [(805, 3), 2378, 18]-NRT-code) | [i] | ||