Information on Result #697147
Linear OA(3262, 1042, F32, 29) (dual of [1042, 980, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,11]) based on
- linear OA(3257, 1025, F32, 29) (dual of [1025, 968, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(3245, 1025, F32, 23) (dual of [1025, 980, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (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(1678, 1042, S16, 29) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(3262, 874, F32, 2, 29) (dual of [(874, 2), 1686, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (33, 62, 874)-net over F32 | [i] | ||
| 4 | Linear OOA(3262, 521, F32, 2, 29) (dual of [(521, 2), 980, 30]-NRT-code) | [i] | OOA Folding | |