Information on Result #691858
Linear OA(16110, 4104, F16, 39) (dual of [4104, 3994, 40]-code), using construction X applied to C([0,19]) ⊂ C([0,18]) based on
- linear OA(16109, 4097, F16, 39) (dual of [4097, 3988, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- 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(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(16110, 3425, F16, 2, 39) (dual of [(3425, 2), 6740, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (71, 110, 3425)-net over F16 | [i] | ||
| 3 | Linear OA(16113, 4142, F16, 39) (dual of [4142, 4029, 40]-code) | [i] | Varšamov–Edel Lengthening | |
| 4 | Linear OA(16114, 4238, F16, 39) (dual of [4238, 4124, 40]-code) | [i] | ||
| 5 | Linear OA(16115, 4456, F16, 39) (dual of [4456, 4341, 40]-code) | [i] | ||
| 6 | Linear OOA(16110, 2052, F16, 2, 39) (dual of [(2052, 2), 3994, 40]-NRT-code) | [i] | OOA Folding | |