Information on Result #696509
Linear OA(3270, 1048606, F32, 17) (dual of [1048606, 1048536, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
- linear OA(3265, 1048577, F32, 17) (dual of [1048577, 1048512, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(3241, 1048577, F32, 11) (dual of [1048577, 1048536, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(325, 29, F32, 5) (dual of [29, 24, 6]-code or 29-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(3270, 1048606, F32, 2, 17) (dual of [(1048606, 2), 2097142, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (53, 70, 1048606)-net over F32 | [i] | ||
| 3 | Linear OOA(3270, 524303, F32, 2, 17) (dual of [(524303, 2), 1048536, 18]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3270, 131075, F32, 17, 17) (dual of [(131075, 17), 2228205, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |