Information on Result #691859
Linear OA(16104, 4104, F16, 37) (dual of [4104, 4000, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,17]) based on
- linear OA(16103, 4097, F16, 37) (dual of [4097, 3994, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(1697, 4097, F16, 35) (dual of [4097, 4000, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (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 OA(16128, 4169, F16, 37) (dual of [4169, 4041, 38]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(16129, 4171, F16, 37) (dual of [4171, 4042, 38]-code) | [i] | ||
| 3 | Linear OA(16130, 4173, F16, 37) (dual of [4173, 4043, 38]-code) | [i] | ||
| 4 | Linear OOA(16104, 3223, F16, 2, 37) (dual of [(3223, 2), 6342, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (67, 104, 3223)-net over F16 | [i] | ||
| 6 | Linear OOA(16104, 2052, F16, 2, 37) (dual of [(2052, 2), 4000, 38]-NRT-code) | [i] | OOA Folding | |