Information on Result #697135
Linear OA(32110, 1042, F32, 53) (dual of [1042, 932, 54]-code), using construction X applied to C([0,26]) ⊂ C([0,23]) based on
- linear OA(32105, 1025, F32, 53) (dual of [1025, 920, 54]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,26], and minimum distance d ≥ |{−26,−25,…,26}|+1 = 54 (BCH-bound) [i]
- linear OA(3293, 1025, F32, 47) (dual of [1025, 932, 48]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,23], and minimum distance d ≥ |{−23,−22,…,23}|+1 = 48 (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 | Linear OOA(32110, 1032, F32, 2, 53) (dual of [(1032, 2), 1954, 54]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (57, 110, 1032)-net over F32 | [i] | ||