Information on Result #699585
Linear OA(8167, 6587, F81, 30) (dual of [6587, 6520, 31]-code), using construction X applied to Ce(29) ⊂ Ce(20) based on
- linear OA(8159, 6561, F81, 30) (dual of [6561, 6502, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(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(8167, 4438, F81, 2, 30) (dual of [(4438, 2), 8809, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8167, 4438, F81, 3, 30) (dual of [(4438, 3), 13247, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(8167, 4438, F81, 4, 30) (dual of [(4438, 4), 17685, 31]-NRT-code) | [i] | ||
| 4 | Digital (37, 67, 4438)-net over F81 | [i] | ||
| 5 | Linear OOA(8167, 3293, F81, 2, 30) (dual of [(3293, 2), 6519, 31]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8167, 2195, F81, 3, 30) (dual of [(2195, 3), 6518, 31]-NRT-code) | [i] | ||