Information on Result #691747
Linear OA(16127, 65559, F16, 33) (dual of [65559, 65432, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,13]) based on
- linear OA(16121, 65537, F16, 33) (dual of [65537, 65416, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 168−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(16105, 65537, F16, 27) (dual of [65537, 65432, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 168−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(166, 22, F16, 5) (dual of [22, 16, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(166, 24, F16, 5) (dual of [24, 18, 6]-code), using
- extended algebraic-geometric code AGe(F,18P) [i] based on function field F/F16 with g(F) = 1 and N(F) ≥ 24, using
- discarding factors / shortening the dual code based on linear OA(166, 24, F16, 5) (dual of [24, 18, 6]-code), 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(16127, 64863, F16, 2, 33) (dual of [(64863, 2), 129599, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (94, 127, 64863)-net over F16 | [i] | ||