Information on Result #699347
Linear OA(8148, 6585, F81, 21) (dual of [6585, 6537, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,6]) based on
- linear OA(8141, 6562, F81, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(8125, 6562, F81, 13) (dual of [6562, 6537, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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(8148, 5205, F81, 2, 21) (dual of [(5205, 2), 10362, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8148, 5205, F81, 3, 21) (dual of [(5205, 3), 15567, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(8148, 5205, F81, 4, 21) (dual of [(5205, 4), 20772, 22]-NRT-code) | [i] | ||
| 4 | Digital (27, 48, 5205)-net over F81 | [i] | ||
| 5 | Linear OOA(8148, 3292, F81, 2, 21) (dual of [(3292, 2), 6536, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8148, 2195, F81, 3, 21) (dual of [(2195, 3), 6537, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(8148, 1646, F81, 4, 21) (dual of [(1646, 4), 6536, 22]-NRT-code) | [i] | ||