Information on Result #1116082
Linear OOA(2257, 1677750, F2, 5, 20) (dual of [(1677750, 5), 8388493, 21]-NRT-code), using (u, u+v)-construction based on
- linear OOA(227, 30, F2, 5, 10) (dual of [(30, 5), 123, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (17, 27, 30)-net over F2, using
- 3 times m-reduction [i] based on digital (17, 30, 30)-net over F2, using
- extracting embedded OOA [i] based on digital (17, 27, 30)-net over F2, using
- linear OOA(2230, 1677720, F2, 5, 20) (dual of [(1677720, 5), 8388370, 21]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2230, 8388600, F2, 20) (dual of [8388600, 8388370, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2230, large, F2, 20) (dual of [large, large−230, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2230, large, F2, 20) (dual of [large, large−230, 21]-code), using
- OOA 5-folding [i] based on linear OA(2230, 8388600, F2, 20) (dual of [8388600, 8388370, 21]-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, 1584865, F2, 6, 20) (dual of [(1584865, 6), 9508933, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2257, 1584865, F2, 7, 20) (dual of [(1584865, 7), 11093798, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(2257, 1584865, F2, 8, 20) (dual of [(1584865, 8), 12678663, 21]-NRT-code) | [i] | ||
| 4 | Digital (237, 257, 1584865)-net over F2 | [i] | ||