Information on Result #1680057
Linear OOA(2106, 4194429, F2, 7, 8) (dual of [(4194429, 7), 29360897, 9]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2106, 4194429, F2, 2, 8) (dual of [(4194429, 2), 8388752, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(214, 128, F2, 2, 4) (dual of [(128, 2), 242, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (10, 14, 128)-net over F2, using
- linear OOA(292, 4194301, F2, 2, 8) (dual of [(4194301, 2), 8388510, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(292, 8388602, F2, 8) (dual of [8388602, 8388510, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- OOA 2-folding [i] based on linear OA(292, 8388602, F2, 8) (dual of [8388602, 8388510, 9]-code), using
- linear OOA(214, 128, F2, 2, 4) (dual of [(128, 2), 242, 5]-NRT-code), using
Mode: 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(2106, 4194429, F2, 8, 8) (dual of [(4194429, 8), 33555326, 9]-NRT-code) | [i] | Appending kth Column | |