Information on Result #2266434
Linear OA(3180, 6581, F3, 33) (dual of [6581, 6401, 34]-code), using 2 times code embedding in larger space based on linear OA(3178, 6579, F3, 33) (dual of [6579, 6401, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,15]) [i] based on
- linear OA(3177, 6562, F3, 33) (dual of [6562, 6385, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (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(31, 17, F3, 1) (dual of [17, 16, 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
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(3180, 3502, F3, 2, 33) (dual of [(3502, 2), 6824, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3180, 3502, F3, 3, 33) (dual of [(3502, 3), 10326, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(3180, 3502, F3, 4, 33) (dual of [(3502, 4), 13828, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(3180, 3502, F3, 5, 33) (dual of [(3502, 5), 17330, 34]-NRT-code) | [i] | ||
| 5 | Digital (147, 180, 3502)-net over F3 | [i] | ||