Information on Result #696735
Linear OA(3282, 32784, F32, 27) (dual of [32784, 32702, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,11]) based on
- linear OA(3279, 32769, F32, 27) (dual of [32769, 32690, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3267, 32769, F32, 23) (dual of [32769, 32702, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(323, 15, F32, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,32) or 15-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 | Linear OA(32102, 32882, F32, 27) (dual of [32882, 32780, 28]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(3282, 24702, F32, 2, 27) (dual of [(24702, 2), 49322, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (55, 82, 24702)-net over F32 | [i] | ||
| 4 | Linear OOA(3282, 16392, F32, 2, 27) (dual of [(16392, 2), 32702, 28]-NRT-code) | [i] | OOA Folding | |