Information on Result #1143925
Linear OOA(2257, 1398129, F2, 6, 21) (dual of [(1398129, 6), 8388517, 22]-NRT-code), using (u, u+v)-construction based on
- linear OOA(226, 29, F2, 6, 10) (dual of [(29, 6), 148, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (16, 26, 29)-net over F2, using
- 3 times m-reduction [i] based on digital (16, 29, 29)-net over F2, using
- extracting embedded OOA [i] based on digital (16, 26, 29)-net over F2, using
- linear OOA(2231, 1398100, F2, 6, 21) (dual of [(1398100, 6), 8388369, 22]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2231, 8388600, F2, 21) (dual of [8388600, 8388369, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2231, large, F2, 21) (dual of [large, large−231, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2231, large, F2, 21) (dual of [large, large−231, 22]-code), using
- OOA 6-folding [i] based on linear OA(2231, 8388600, F2, 21) (dual of [8388600, 8388369, 22]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2257, 1398129, F2, 7, 21) (dual of [(1398129, 7), 9786646, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2257, 1398129, F2, 8, 21) (dual of [(1398129, 8), 11184775, 22]-NRT-code) | [i] | ||
| 3 | Digital (236, 257, 1398129)-net over F2 | [i] | ||