Information on Result #873526
Linear OOA(4938, 1203, F49, 2, 19) (dual of [(1203, 2), 2368, 20]-NRT-code), using OOA 2-folding based on linear OA(4938, 2406, F49, 19) (dual of [2406, 2368, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4938, 2407, F49, 19) (dual of [2407, 2369, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] 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(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(491, 5, F49, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,9]) ⊂ C([0,8]) [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(4947, 1253, F49, 2, 19) (dual of [(1253, 2), 2459, 20]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(4948, 1254, F49, 2, 19) (dual of [(1254, 2), 2460, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(4949, 1255, F49, 2, 19) (dual of [(1255, 2), 2461, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(4951, 1303, F49, 2, 19) (dual of [(1303, 2), 2555, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(4952, 1304, F49, 2, 19) (dual of [(1304, 2), 2556, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(4938, 893, F49, 3, 19) (dual of [(893, 3), 2641, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Digital (19, 38, 893)-net over F49 | [i] | ||