Information on Result #699354
Linear OA(8166, 6591, F81, 29) (dual of [6591, 6525, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,9]) based on
- linear OA(8157, 6562, F81, 29) (dual of [6562, 6505, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(819, 29, F81, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,81)), using
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), using
- Reed–Solomon code RS(72,81) [i]
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), 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(8166, 5355, F81, 2, 29) (dual of [(5355, 2), 10644, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8166, 5355, F81, 3, 29) (dual of [(5355, 3), 15999, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(8166, 5355, F81, 4, 29) (dual of [(5355, 4), 21354, 30]-NRT-code) | [i] | ||
| 4 | Digital (37, 66, 5355)-net over F81 | [i] | ||
| 5 | Linear OOA(8166, 3295, F81, 2, 29) (dual of [(3295, 2), 6524, 30]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8166, 2197, F81, 3, 29) (dual of [(2197, 3), 6525, 30]-NRT-code) | [i] | ||
| 7 | Linear OOA(8166, 1647, F81, 4, 29) (dual of [(1647, 4), 6522, 30]-NRT-code) | [i] | ||