Information on Result #895024
Linear OOA(3128, 4194310, F3, 2, 12) (dual of [(4194310, 2), 8388492, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(38, 9, F3, 2, 6) (dual of [(9, 2), 10, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (2, 8, 9)-net over F3, using
- 1 times m-reduction [i] based on digital (2, 9, 9)-net over F3, using
- extracting embedded OOA [i] based on digital (2, 8, 9)-net over F3, using
- linear OOA(3120, 4194301, F3, 2, 12) (dual of [(4194301, 2), 8388482, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3120, 8388602, F3, 12) (dual of [8388602, 8388482, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- OOA 2-folding [i] based on linear OA(3120, 8388602, F3, 12) (dual of [8388602, 8388482, 13]-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(3128, 4194310, F3, 3, 12) (dual of [(4194310, 3), 12582802, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3128, 4194310, F3, 4, 12) (dual of [(4194310, 4), 16777112, 13]-NRT-code) | [i] | ||
| 3 | Linear OOA(3128, 4194310, F3, 5, 12) (dual of [(4194310, 5), 20971422, 13]-NRT-code) | [i] | ||
| 4 | Digital (116, 128, 4194310)-net over F3 | [i] | ||
| 5 | Linear OOA(3128, 2097155, F3, 4, 12) (dual of [(2097155, 4), 8388492, 13]-NRT-code) | [i] | OOA Folding | |