Information on Result #675304
Linear OA(3229, 6582, F3, 42) (dual of [6582, 6353, 43]-code), using construction X applied to C([0,21]) ⊂ C([0,19]) based on
- linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(3209, 6562, F3, 39) (dual of [6562, 6353, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (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(3229, 4096, F3, 2, 42) (dual of [(4096, 2), 7963, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3229, 4096, F3, 3, 42) (dual of [(4096, 3), 12059, 43]-NRT-code) | [i] | ||
| 3 | Linear OOA(3229, 4096, F3, 4, 42) (dual of [(4096, 4), 16155, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(3229, 4096, F3, 5, 42) (dual of [(4096, 5), 20251, 43]-NRT-code) | [i] | ||
| 5 | Digital (187, 229, 4096)-net over F3 | [i] | ||
| 6 | Linear OOA(3229, 3291, F3, 2, 42) (dual of [(3291, 2), 6353, 43]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3229, 2194, F3, 3, 42) (dual of [(2194, 3), 6353, 43]-NRT-code) | [i] | ||