Information on Result #1116080
Linear OOA(2255, 1677747, F2, 5, 20) (dual of [(1677747, 5), 8388480, 21]-NRT-code), using (u, u+v)-construction based on
- linear OOA(225, 27, F2, 5, 10) (dual of [(27, 5), 110, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 25, 27)-net over F2, using
- 2 times m-reduction [i] based on digital (15, 27, 27)-net over F2, using
- extracting embedded OOA [i] based on digital (15, 25, 27)-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(2255, 1435448, F2, 6, 20) (dual of [(1435448, 6), 8612433, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2255, 1435448, F2, 7, 20) (dual of [(1435448, 7), 10047881, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(2255, 1435448, F2, 8, 20) (dual of [(1435448, 8), 11483329, 21]-NRT-code) | [i] | ||
| 4 | Digital (235, 255, 1435448)-net over F2 | [i] | ||
| 5 | Linear OOA(2255, 838873, F2, 25, 20) (dual of [(838873, 25), 20971570, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |