Information on Result #699612
Linear OA(8171, 6593, F81, 31) (dual of [6593, 6522, 32]-code), using construction X applied to Ce(30) ⊂ Ce(19) based on
- linear OA(8161, 6561, F81, 31) (dual of [6561, 6500, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8110, 32, F81, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,81)), using
- discarding factors / shortening the dual code based on linear OA(8110, 81, F81, 10) (dual of [81, 71, 11]-code or 81-arc in PG(9,81)), using
- Reed–Solomon code RS(71,81) [i]
- discarding factors / shortening the dual code based on linear OA(8110, 81, F81, 10) (dual of [81, 71, 11]-code or 81-arc in PG(9,81)), 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(8171, 5884, F81, 2, 31) (dual of [(5884, 2), 11697, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8171, 5884, F81, 3, 31) (dual of [(5884, 3), 17581, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(8171, 5884, F81, 4, 31) (dual of [(5884, 4), 23465, 32]-NRT-code) | [i] | ||
| 4 | Digital (40, 71, 5884)-net over F81 | [i] | ||
| 5 | Linear OOA(8171, 3296, F81, 2, 31) (dual of [(3296, 2), 6521, 32]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8171, 1648, F81, 4, 31) (dual of [(1648, 4), 6521, 32]-NRT-code) | [i] | ||