Information on Result #894073
Linear OOA(2108, 4194558, F2, 2, 8) (dual of [(4194558, 2), 8389008, 9]-NRT-code), using (u, u+v)-construction based on
- linear OOA(216, 257, F2, 2, 4) (dual of [(257, 2), 498, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 16, 257)-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
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(2108, 4194558, F2, 3, 8) (dual of [(4194558, 3), 12583566, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2108, 4194558, F2, 4, 8) (dual of [(4194558, 4), 16778124, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(2108, 4194558, F2, 5, 8) (dual of [(4194558, 5), 20972682, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(2108, 4194558, F2, 6, 8) (dual of [(4194558, 6), 25167240, 9]-NRT-code) | [i] | ||
| 5 | Linear OOA(2108, 4194558, F2, 7, 8) (dual of [(4194558, 7), 29361798, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(2108, 2097279, F2, 4, 8) (dual of [(2097279, 4), 8389008, 9]-NRT-code) | [i] | OOA Folding | |