Information on Result #699610
Linear OA(8175, 6593, F81, 33) (dual of [6593, 6518, 34]-code), using construction X applied to Ce(32) ⊂ Ce(21) based on
- linear OA(8165, 6561, F81, 33) (dual of [6561, 6496, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(8175, 5566, F81, 2, 33) (dual of [(5566, 2), 11057, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8175, 5566, F81, 3, 33) (dual of [(5566, 3), 16623, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(8175, 5566, F81, 4, 33) (dual of [(5566, 4), 22189, 34]-NRT-code) | [i] | ||
| 4 | Digital (42, 75, 5566)-net over F81 | [i] | ||
| 5 | Linear OOA(8175, 3296, F81, 2, 33) (dual of [(3296, 2), 6517, 34]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8175, 1648, F81, 4, 33) (dual of [(1648, 4), 6517, 34]-NRT-code) | [i] | ||