Information on Result #691551
Linear OA(1654, 1048595, F16, 11) (dual of [1048595, 1048541, 12]-code), using construction X applied to C([0,5]) ⊂ C([0,3]) based on
- linear OA(1651, 1048577, F16, 11) (dual of [1048577, 1048526, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 1610−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(1631, 1048577, F16, 7) (dual of [1048577, 1048546, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 1610−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(163, 18, F16, 3) (dual of [18, 15, 4]-code or 18-arc in PG(2,16) or 18-cap in PG(2,16)), 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(1654, 1048595, F16, 2, 11) (dual of [(1048595, 2), 2097136, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (43, 54, 1048595)-net over F16 | [i] | ||
| 3 | Linear OOA(1654, 524297, F16, 2, 11) (dual of [(524297, 2), 1048540, 12]-NRT-code) | [i] | OOA Folding | |