Information on Result #698177
Linear OA(4940, 2413, F49, 19) (dual of [2413, 2373, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,7]) based on
- linear OA(4937, 2402, F49, 19) (dual of [2402, 2365, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 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(493, 11, F49, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,49) or 11-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), 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 OA(4949, 2463, F49, 19) (dual of [2463, 2414, 20]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(4940, 1206, F49, 2, 19) (dual of [(1206, 2), 2372, 20]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(4940, 804, F49, 3, 19) (dual of [(804, 3), 2372, 20]-NRT-code) | [i] | ||