Information on Result #699477
Linear OA(8117, 6569, F81, 8) (dual of [6569, 6552, 9]-code), using construction X applied to Ce(7) ⊂ Ce(4) based on
- linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(819, 6561, F81, 5) (dual of [6561, 6552, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), 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 OA(934, 13138, F9, 8) (dual of [13138, 13104, 9]-code) | [i] | Trace Code | |
| 2 | Linear OOA(8117, 4594, F81, 2, 8) (dual of [(4594, 2), 9171, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8117, 4594, F81, 3, 8) (dual of [(4594, 3), 13765, 9]-NRT-code) | [i] | ||
| 4 | Linear OOA(8117, 4594, F81, 4, 8) (dual of [(4594, 4), 18359, 9]-NRT-code) | [i] | ||
| 5 | Digital (9, 17, 4594)-net over F81 | [i] | ||
| 6 | Linear OOA(8117, 3284, F81, 2, 8) (dual of [(3284, 2), 6551, 9]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8117, 2189, F81, 3, 8) (dual of [(2189, 3), 6550, 9]-NRT-code) | [i] | ||
| 8 | Linear OOA(8117, 1642, F81, 4, 8) (dual of [(1642, 4), 6551, 9]-NRT-code) | [i] | ||
| 9 | Linear OOA(8117, 1642, F81, 8, 8) (dual of [(1642, 8), 13119, 9]-NRT-code) | [i] | OA Folding and Stacking | |