Information on Result #697131
Linear OA(3232, 1036, F32, 15) (dual of [1036, 1004, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,5]) based on
- linear OA(3229, 1025, F32, 15) (dual of [1025, 996, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(3221, 1025, F32, 11) (dual of [1025, 1004, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(323, 11, F32, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,32) or 11-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), 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(1640, 1036, S16, 15) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(3232, 704, F32, 2, 15) (dual of [(704, 2), 1376, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (17, 32, 704)-net over F32 | [i] | ||
| 4 | Linear OOA(3232, 518, F32, 2, 15) (dual of [(518, 2), 1004, 16]-NRT-code) | [i] | OOA Folding | |