Information on Result #812613
Linear OOA(338, 9847, F3, 2, 7) (dual of [(9847, 2), 19656, 8]-NRT-code), using OOA 2-folding based on linear OA(338, 19694, F3, 7) (dual of [19694, 19656, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(337, 19683, F3, 7) (dual of [19683, 19646, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(328, 19683, F3, 5) (dual of [19683, 19655, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(310, 11, F3, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,3)), using
- dual of repetition code with length 11 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(340, 9848, F3, 2, 7) (dual of [(9848, 2), 19656, 8]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(339, 9847, F3, 2, 7) (dual of [(9847, 2), 19655, 8]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(338, 9847, F3, 3, 7) (dual of [(9847, 3), 29503, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(338, 9847, F3, 4, 7) (dual of [(9847, 4), 39350, 8]-NRT-code) | [i] | ||
| 5 | Linear OOA(338, 9847, F3, 5, 7) (dual of [(9847, 5), 49197, 8]-NRT-code) | [i] | ||
| 6 | Digital (31, 38, 9847)-net over F3 | [i] | ||