Information on Result #873473
Linear OOA(4936, 1206, F49, 2, 17) (dual of [(1206, 2), 2376, 18]-NRT-code), using OOA 2-folding based on linear OA(4936, 2412, F49, 17) (dual of [2412, 2376, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4936, 2413, F49, 17) (dual of [2413, 2377, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(4933, 2402, F49, 17) (dual of [2402, 2369, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(4925, 2402, F49, 13) (dual of [2402, 2377, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
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(4944, 1256, F49, 2, 17) (dual of [(1256, 2), 2468, 18]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(4936, 1206, F49, 3, 17) (dual of [(1206, 3), 3582, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (19, 36, 1206)-net over F49 | [i] | ||