Information on Result #1568323
Linear OOA(2181, 2804393, F2, 3, 13) (dual of [(2804393, 3), 8412998, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(242, 8192, F2, 3, 6) (dual of [(8192, 3), 24534, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(242, 8192, F2, 2, 6) (dual of [(8192, 2), 16342, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(240, 8191, F2, 2, 6) (dual of [(8191, 2), 16342, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F2, using
- 1 times m-reduction [i] based on digital (34, 41, 8191)-net over F2, using
- extracting embedded OOA [i] based on digital (34, 40, 8191)-net over F2, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(240, 8191, F2, 2, 6) (dual of [(8191, 2), 16342, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(242, 8192, F2, 2, 6) (dual of [(8192, 2), 16342, 7]-NRT-code), using
- linear OOA(2139, 2796201, F2, 3, 13) (dual of [(2796201, 3), 8388464, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-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(2181, 2804393, F2, 4, 13) (dual of [(2804393, 4), 11217391, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2181, 2804393, F2, 5, 13) (dual of [(2804393, 5), 14021784, 14]-NRT-code) | [i] | ||
| 3 | Linear OOA(2181, 2804393, F2, 6, 13) (dual of [(2804393, 6), 16826177, 14]-NRT-code) | [i] | ||
| 4 | Linear OOA(2181, 2804393, F2, 7, 13) (dual of [(2804393, 7), 19630570, 14]-NRT-code) | [i] | ||
| 5 | Linear OOA(2181, 2804393, F2, 8, 13) (dual of [(2804393, 8), 22434963, 14]-NRT-code) | [i] | ||
| 6 | Digital (168, 181, 2804393)-net over F2 | [i] | ||