Information on Result #697146
Linear OA(3266, 1042, F32, 31) (dual of [1042, 976, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,12]) based on
- linear OA(3261, 1025, F32, 31) (dual of [1025, 964, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3249, 1025, F32, 25) (dual of [1025, 976, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(325, 17, F32, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), 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 | OA(1683, 1042, S16, 31) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(3266, 876, F32, 2, 31) (dual of [(876, 2), 1686, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (35, 66, 876)-net over F32 | [i] | ||
| 4 | Linear OOA(3266, 521, F32, 2, 31) (dual of [(521, 2), 976, 32]-NRT-code) | [i] | OOA Folding | |