Information on Result #686184
Linear OA(8170, 2097168, F8, 27) (dual of [2097168, 2096998, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,12]) based on
- linear OA(8169, 2097153, F8, 27) (dual of [2097153, 2096984, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(8155, 2097153, F8, 25) (dual of [2097153, 2096998, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 814−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(81, 15, F8, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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(8170, 1851026, F8, 2, 27) (dual of [(1851026, 2), 3701882, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8170, 1851026, F8, 3, 27) (dual of [(1851026, 3), 5552908, 28]-NRT-code) | [i] | ||
| 3 | Digital (143, 170, 1851026)-net over F8 | [i] | ||