Information on Result #895316
Linear OOA(3228, 4194321, F3, 2, 21) (dual of [(4194321, 2), 8388414, 22]-NRT-code), using (u, u+v)-construction based on
- linear OOA(318, 20, F3, 2, 10) (dual of [(20, 2), 22, 11]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 18, 20)-net over F3, using
- 2 times m-reduction [i] based on digital (8, 20, 20)-net over F3, using
- extracting embedded OOA [i] based on digital (8, 18, 20)-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(3228, 3695051, F3, 3, 21) (dual of [(3695051, 3), 11084925, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3228, 3695051, F3, 4, 21) (dual of [(3695051, 4), 14779976, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(3228, 3695051, F3, 5, 21) (dual of [(3695051, 5), 18475027, 22]-NRT-code) | [i] | ||
| 4 | Digital (207, 228, 3695051)-net over F3 | [i] | ||
| 5 | Linear OOA(3228, 2097160, F3, 4, 21) (dual of [(2097160, 4), 8388412, 22]-NRT-code) | [i] | OOA Folding | |