Information on Result #2487572
Linear OOA(3197, 9858, F3, 2, 32) (dual of [(9858, 2), 19519, 33]-NRT-code), using 31 times duplication based on linear OOA(3196, 9858, F3, 2, 32) (dual of [(9858, 2), 19520, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3196, 19716, F3, 32) (dual of [19716, 19520, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(27) [i] based on
- linear OA(3190, 19683, F3, 32) (dual of [19683, 19493, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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
- construction X applied to Ce(31) ⊂ Ce(27) [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(3197, 9398, F3, 3, 32) (dual of [(9398, 3), 27997, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3197, 9398, F3, 4, 32) (dual of [(9398, 4), 37395, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3197, 9398, F3, 5, 32) (dual of [(9398, 5), 46793, 33]-NRT-code) | [i] | ||
| 4 | Digital (165, 197, 9398)-net over F3 | [i] | ||