Information on Result #1143898
Linear OOA(2251, 1398123, F2, 6, 20) (dual of [(1398123, 6), 8388487, 21]-NRT-code), using (u, u+v)-construction based on
- linear OOA(221, 23, F2, 6, 10) (dual of [(23, 6), 117, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (11, 21, 23)-net over F2, using
- linear OOA(2230, 1398100, F2, 6, 20) (dual of [(1398100, 6), 8388370, 21]-NRT-code), using
- OOA 6-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 6-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(2251, 1398123, F2, 7, 20) (dual of [(1398123, 7), 9786610, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2251, 1398123, F2, 8, 20) (dual of [(1398123, 8), 11184733, 21]-NRT-code) | [i] | ||
| 3 | Digital (231, 251, 1398123)-net over F2 | [i] | ||