Information on Result #675373
Linear OA(3197, 6598, F3, 34) (dual of [6598, 6401, 35]-code), using construction X applied to C([0,18]) ⊂ C([0,15]) based on
- linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3161, 6562, F3, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(34, 36, F3, 2) (dual of [36, 32, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), 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(3197, 5318, F3, 2, 34) (dual of [(5318, 2), 10439, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3197, 5318, F3, 3, 34) (dual of [(5318, 3), 15757, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(3197, 5318, F3, 4, 34) (dual of [(5318, 4), 21075, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(3197, 5318, F3, 5, 34) (dual of [(5318, 5), 26393, 35]-NRT-code) | [i] | ||
| 5 | Digital (163, 197, 5318)-net over F3 | [i] | ||