Information on Result #675322
Linear OA(3165, 6582, F3, 30) (dual of [6582, 6417, 31]-code), using construction X applied to C([0,15]) ⊂ C([0,13]) based on
- 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(3145, 6562, F3, 27) (dual of [6562, 6417, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(34, 20, F3, 2) (dual of [20, 16, 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(3165, 3494, F3, 2, 30) (dual of [(3494, 2), 6823, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3165, 3494, F3, 3, 30) (dual of [(3494, 3), 10317, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(3165, 3494, F3, 4, 30) (dual of [(3494, 4), 13811, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(3165, 3494, F3, 5, 30) (dual of [(3494, 5), 17305, 31]-NRT-code) | [i] | ||
| 5 | Digital (135, 165, 3494)-net over F3 | [i] | ||
| 6 | Linear OOA(3165, 3291, F3, 2, 30) (dual of [(3291, 2), 6417, 31]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3165, 2194, F3, 3, 30) (dual of [(2194, 3), 6417, 31]-NRT-code) | [i] | ||