Information on Result #895319
Linear OOA(3231, 4194326, F3, 2, 21) (dual of [(4194326, 2), 8388421, 22]-NRT-code), using (u, u+v)-construction based on
- linear OOA(321, 25, F3, 2, 10) (dual of [(25, 2), 29, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (11, 21, 25)-net over F3, using
- 4 times m-reduction [i] based on digital (11, 25, 25)-net over F3, using
- extracting embedded OOA [i] based on digital (11, 21, 25)-net over F3, using
- linear OOA(3210, 4194301, F3, 2, 21) (dual of [(4194301, 2), 8388392, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3210, 8388602, F3, 21) (dual of [8388602, 8388392, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(3210, large, F3, 21) (dual of [large, large−210, 22]-code), using
- OOA 2-folding [i] based on linear OA(3210, 8388602, F3, 21) (dual of [8388602, 8388392, 22]-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(3231, 4194326, F3, 3, 21) (dual of [(4194326, 3), 12582747, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3231, 4194326, F3, 4, 21) (dual of [(4194326, 4), 16777073, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(3231, 4194326, F3, 5, 21) (dual of [(4194326, 5), 20971399, 22]-NRT-code) | [i] | ||
| 4 | Digital (210, 231, 4194326)-net over F3 | [i] | ||
| 5 | Linear OOA(3231, 2097163, F3, 4, 21) (dual of [(2097163, 4), 8388421, 22]-NRT-code) | [i] | OOA Folding | |