Information on Result #895227
Linear OOA(3197, 4194321, F3, 2, 18) (dual of [(4194321, 2), 8388445, 19]-NRT-code), using (u, u+v)-construction based on
- linear OOA(317, 20, F3, 2, 9) (dual of [(20, 2), 23, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 17, 20)-net over F3, using
- 3 times m-reduction [i] based on digital (8, 20, 20)-net over F3, using
- extracting embedded OOA [i] based on digital (8, 17, 20)-net over F3, using
- linear OOA(3180, 4194301, F3, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(3180, large, F3, 18) (dual of [large, large−180, 19]-code), using
- OOA 2-folding [i] based on linear OA(3180, 8388602, F3, 18) (dual of [8388602, 8388422, 19]-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(3197, 4194321, F3, 3, 18) (dual of [(4194321, 3), 12582766, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3197, 4194321, F3, 4, 18) (dual of [(4194321, 4), 16777087, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(3197, 4194321, F3, 5, 18) (dual of [(4194321, 5), 20971408, 19]-NRT-code) | [i] | ||
| 4 | Digital (179, 197, 4194321)-net over F3 | [i] | ||
| 5 | Linear OOA(3197, 2097160, F3, 4, 18) (dual of [(2097160, 4), 8388443, 19]-NRT-code) | [i] | OOA Folding | |