Information on Result #699345
Linear OA(8156, 6585, F81, 25) (dual of [6585, 6529, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,8]) based on
- linear OA(8149, 6562, F81, 25) (dual of [6562, 6513, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(8133, 6562, F81, 17) (dual of [6562, 6529, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(817, 23, F81, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,81)), using
- discarding factors / shortening the dual code based on linear OA(817, 81, F81, 7) (dual of [81, 74, 8]-code or 81-arc in PG(6,81)), using
- Reed–Solomon code RS(74,81) [i]
- discarding factors / shortening the dual code based on linear OA(817, 81, F81, 7) (dual of [81, 74, 8]-code or 81-arc in PG(6,81)), 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(8156, 4306, F81, 2, 25) (dual of [(4306, 2), 8556, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8156, 4306, F81, 3, 25) (dual of [(4306, 3), 12862, 26]-NRT-code) | [i] | ||
| 3 | Linear OOA(8156, 4306, F81, 4, 25) (dual of [(4306, 4), 17168, 26]-NRT-code) | [i] | ||
| 4 | Digital (31, 56, 4306)-net over F81 | [i] | ||
| 5 | Linear OOA(8156, 3292, F81, 2, 25) (dual of [(3292, 2), 6528, 26]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8156, 2195, F81, 3, 25) (dual of [(2195, 3), 6529, 26]-NRT-code) | [i] | ||
| 7 | Linear OOA(8156, 1646, F81, 4, 25) (dual of [(1646, 4), 6528, 26]-NRT-code) | [i] | ||