Information on Result #691855
Linear OA(16128, 4104, F16, 45) (dual of [4104, 3976, 46]-code), using construction X applied to C([0,22]) ⊂ C([0,21]) based on
- linear OA(16127, 4097, F16, 45) (dual of [4097, 3970, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- linear OA(16121, 4097, F16, 43) (dual of [4097, 3976, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(161, 7, F16, 1) (dual of [7, 6, 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 OOA(16128, 4030, F16, 2, 45) (dual of [(4030, 2), 7932, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (83, 128, 4030)-net over F16 | [i] | ||
| 3 | Linear OOA(16128, 2052, F16, 2, 45) (dual of [(2052, 2), 3976, 46]-NRT-code) | [i] | OOA Folding | |