Information on Result #895288
Linear OOA(3215, 4194322, F3, 2, 20) (dual of [(4194322, 2), 8388429, 21]-NRT-code), using (u, u+v)-construction based on
- linear OOA(319, 21, F3, 2, 10) (dual of [(21, 2), 23, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (9, 19, 21)-net over F3, using
- 2 times m-reduction [i] based on digital (9, 21, 21)-net over F3, using
- extracting embedded OOA [i] based on digital (9, 19, 21)-net over F3, using
- linear OOA(3196, 4194301, F3, 2, 20) (dual of [(4194301, 2), 8388406, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3196, 8388602, F3, 20) (dual of [8388602, 8388406, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3196, large, F3, 20) (dual of [large, large−196, 21]-code), using
- OOA 2-folding [i] based on linear OA(3196, 8388602, F3, 20) (dual of [8388602, 8388406, 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(3215, 3411629, F3, 3, 20) (dual of [(3411629, 3), 10234672, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3215, 3411629, F3, 4, 20) (dual of [(3411629, 4), 13646301, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(3215, 3411629, F3, 5, 20) (dual of [(3411629, 5), 17057930, 21]-NRT-code) | [i] | ||
| 4 | Digital (195, 215, 3411629)-net over F3 | [i] | ||
| 5 | Linear OOA(3215, 2097161, F3, 4, 20) (dual of [(2097161, 4), 8388429, 21]-NRT-code) | [i] | OOA Folding | |