Information on Result #698264
Linear OA(4917, 2409, F49, 8) (dual of [2409, 2392, 9]-code), using construction X applied to Ce(7) ⊂ Ce(4) based on
- linear OA(4915, 2401, F49, 8) (dual of [2401, 2386, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(499, 2401, F49, 5) (dual of [2401, 2392, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(492, 8, F49, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), 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(4917, 2003, F49, 2, 8) (dual of [(2003, 2), 3989, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4917, 2003, F49, 3, 8) (dual of [(2003, 3), 5992, 9]-NRT-code) | [i] | ||
| 3 | Digital (9, 17, 2003)-net over F49 | [i] | ||
| 4 | Linear OOA(4917, 1204, F49, 2, 8) (dual of [(1204, 2), 2391, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4917, 803, F49, 3, 8) (dual of [(803, 3), 2392, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(4917, 602, F49, 8, 8) (dual of [(602, 8), 4799, 9]-NRT-code) | [i] | OA Folding and Stacking | |