Information on Result #663327
Linear OA(7105, 5764813, F7, 15) (dual of [5764813, 5764708, 16]-code), using (u, u+v)-construction based on
- linear OA(78, 11, F7, 7) (dual of [11, 3, 8]-code), using
- construction X applied to C1 ⊂ C0 [i] based on
- linear OA(77, 8, F7, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,7)), using code C1 for u = 2 by de Boer and Brouwer [i]
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using code C0 for u = 2 by de Boer and Brouwer [i]
- linear OA(71, 3, F7, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C1 ⊂ C0 [i] based on
- linear OA(797, 5764802, F7, 15) (dual of [5764802, 5764705, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 5764802 | 716−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
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(7105, 5445511, F7, 2, 15) (dual of [(5445511, 2), 10890917, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(7105, 5445511, F7, 3, 15) (dual of [(5445511, 3), 16336428, 16]-NRT-code) | [i] | ||
| 3 | Digital (90, 105, 5445511)-net over F7 | [i] | ||