Information on Result #698188
Linear OA(4934, 2419, F49, 15) (dual of [2419, 2385, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,4]) based on
- linear OA(4929, 2402, F49, 15) (dual of [2402, 2373, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(4917, 2402, F49, 9) (dual of [2402, 2385, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(495, 17, F49, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,49)), using
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), using
- Reed–Solomon code RS(44,49) [i]
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), 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(4934, 2299, F49, 2, 15) (dual of [(2299, 2), 4564, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4934, 2299, F49, 3, 15) (dual of [(2299, 3), 6863, 16]-NRT-code) | [i] | ||
| 3 | Digital (19, 34, 2299)-net over F49 | [i] | ||
| 4 | Linear OOA(4934, 1209, F49, 2, 15) (dual of [(1209, 2), 2384, 16]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4934, 806, F49, 3, 15) (dual of [(806, 3), 2384, 16]-NRT-code) | [i] | ||
| 6 | Linear OOA(4934, 345, F49, 15, 15) (dual of [(345, 15), 5141, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |