Information on Result #699611
Linear OA(8173, 6593, F81, 32) (dual of [6593, 6520, 33]-code), using construction X applied to Ce(31) ⊂ Ce(20) based on
- linear OA(8163, 6561, F81, 32) (dual of [6561, 6498, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(8141, 6561, F81, 21) (dual of [6561, 6520, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(8173, 5715, F81, 2, 32) (dual of [(5715, 2), 11357, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8173, 5715, F81, 3, 32) (dual of [(5715, 3), 17072, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(8173, 5715, F81, 4, 32) (dual of [(5715, 4), 22787, 33]-NRT-code) | [i] | ||
| 4 | Digital (41, 73, 5715)-net over F81 | [i] | ||
| 5 | Linear OOA(8173, 3296, F81, 2, 32) (dual of [(3296, 2), 6519, 33]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8173, 2197, F81, 3, 32) (dual of [(2197, 3), 6518, 33]-NRT-code) | [i] | ||
| 7 | Linear OOA(8173, 1648, F81, 4, 32) (dual of [(1648, 4), 6519, 33]-NRT-code) | [i] | ||