Information on Result #1702044
Linear OOA(2197, 1398109, F2, 8, 17) (dual of [(1398109, 8), 11184675, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2197, 1398109, F2, 6, 17) (dual of [(1398109, 6), 8388457, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(212, 9, F2, 6, 8) (dual of [(9, 6), 42, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 12, 9)-net over F2, using
- linear OOA(2185, 1398100, F2, 6, 17) (dual of [(1398100, 6), 8388415, 18]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 6-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- linear OOA(212, 9, F2, 6, 8) (dual of [(9, 6), 42, 9]-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(2197, 1398108, F2, 24, 17) (dual of [(1398108, 24), 33554395, 18]-NRT-code) | [i] | OOA Stacking with Additional Row | |