Information on Result #699599
Linear OA(8176, 6590, F81, 34) (dual of [6590, 6514, 35]-code), using construction X applied to Ce(33) ⊂ Ce(23) based on
- linear OA(8167, 6561, F81, 34) (dual of [6561, 6494, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(8147, 6561, F81, 24) (dual of [6561, 6514, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(8176, 4736, F81, 2, 34) (dual of [(4736, 2), 9396, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8176, 4736, F81, 3, 34) (dual of [(4736, 3), 14132, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(8176, 4736, F81, 4, 34) (dual of [(4736, 4), 18868, 35]-NRT-code) | [i] | ||
| 4 | Digital (42, 76, 4736)-net over F81 | [i] | ||
| 5 | Linear OOA(8176, 3295, F81, 2, 34) (dual of [(3295, 2), 6514, 35]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8176, 2196, F81, 3, 34) (dual of [(2196, 3), 6512, 35]-NRT-code) | [i] | ||
| 7 | Linear OOA(8176, 1647, F81, 4, 34) (dual of [(1647, 4), 6512, 35]-NRT-code) | [i] | ||