Information on Result #812922
Linear OOA(375, 9852, F3, 2, 12) (dual of [(9852, 2), 19629, 13]-NRT-code), using OOA 2-folding based on linear OA(375, 19704, F3, 12) (dual of [19704, 19629, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(374, 19703, F3, 12) (dual of [19703, 19629, 13]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
- linear OA(373, 19683, F3, 13) (dual of [19683, 19610, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(355, 19683, F3, 10) (dual of [19683, 19628, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(319, 20, F3, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,3)), using
- dual of repetition code with length 20 [i]
- linear OA(31, 20, F3, 1) (dual of [20, 19, 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
- construction X4 applied to Ce(12) ⊂ Ce(9) [i] based on
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(377, 9853, F3, 2, 12) (dual of [(9853, 2), 19629, 13]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(376, 9852, F3, 2, 12) (dual of [(9852, 2), 19628, 13]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(375, 9852, F3, 3, 12) (dual of [(9852, 3), 29481, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(375, 9852, F3, 4, 12) (dual of [(9852, 4), 39333, 13]-NRT-code) | [i] | ||
| 5 | Linear OOA(375, 9852, F3, 5, 12) (dual of [(9852, 5), 49185, 13]-NRT-code) | [i] | ||
| 6 | Digital (63, 75, 9852)-net over F3 | [i] | ||