Information on Result #699583
Linear OA(8171, 6587, F81, 32) (dual of [6587, 6516, 33]-code), using construction X applied to Ce(31) ⊂ Ce(22) 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(8145, 6561, F81, 23) (dual of [6561, 6516, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(818, 26, F81, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,81)), using
- discarding factors / shortening the dual code based on linear OA(818, 81, F81, 8) (dual of [81, 73, 9]-code or 81-arc in PG(7,81)), using
- Reed–Solomon code RS(73,81) [i]
- discarding factors / shortening the dual code based on linear OA(818, 81, F81, 8) (dual of [81, 73, 9]-code or 81-arc in PG(7,81)), 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, 4260, F81, 2, 32) (dual of [(4260, 2), 8449, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8171, 4260, F81, 3, 32) (dual of [(4260, 3), 12709, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(8171, 4260, F81, 4, 32) (dual of [(4260, 4), 16969, 33]-NRT-code) | [i] | ||
| 4 | Digital (39, 71, 4260)-net over F81 | [i] | ||
| 5 | Linear OOA(8171, 3293, F81, 2, 32) (dual of [(3293, 2), 6515, 33]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8171, 2195, F81, 3, 32) (dual of [(2195, 3), 6514, 33]-NRT-code) | [i] | ||