Information on Result #691530
Linear OA(1662, 1048588, F16, 13) (dual of [1048588, 1048526, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,5]) based on
- linear OA(1661, 1048577, F16, 13) (dual of [1048577, 1048516, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 1610−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 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(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(1670, 1048621, F16, 13) (dual of [1048621, 1048551, 14]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(1662, 1048588, F16, 2, 13) (dual of [(1048588, 2), 2097114, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (49, 62, 1048588)-net over F16 | [i] | ||
| 4 | Linear OOA(1662, 524294, F16, 2, 13) (dual of [(524294, 2), 1048526, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1662, 174764, F16, 13, 13) (dual of [(174764, 13), 2271870, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |