Information on Result #813357
Linear OOA(3106, 9858, F3, 2, 17) (dual of [(9858, 2), 19610, 18]-NRT-code), using OOA 2-folding based on linear OA(3106, 19716, F3, 17) (dual of [19716, 19610, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(3100, 19683, F3, 17) (dual of [19683, 19583, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- 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(36, 33, F3, 3) (dual of [33, 27, 4]-code or 33-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(3108, 9859, F3, 2, 17) (dual of [(9859, 2), 19610, 18]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3107, 9858, F3, 2, 17) (dual of [(9858, 2), 19609, 18]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3106, 9858, F3, 3, 17) (dual of [(9858, 3), 29468, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3106, 9858, F3, 4, 17) (dual of [(9858, 4), 39326, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(3106, 9858, F3, 5, 17) (dual of [(9858, 5), 49184, 18]-NRT-code) | [i] | ||
| 6 | Digital (89, 106, 9858)-net over F3 | [i] | ||