Information on Result #699578
Linear OA(8181, 6587, F81, 37) (dual of [6587, 6506, 38]-code), using construction X applied to Ce(36) ⊂ Ce(27) based on
- linear OA(8173, 6561, F81, 37) (dual of [6561, 6488, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(8155, 6561, F81, 28) (dual of [6561, 6506, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(8181, 3987, F81, 2, 37) (dual of [(3987, 2), 7893, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8181, 3987, F81, 3, 37) (dual of [(3987, 3), 11880, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(8181, 3987, F81, 4, 37) (dual of [(3987, 4), 15867, 38]-NRT-code) | [i] | ||
| 4 | Digital (44, 81, 3987)-net over F81 | [i] | ||
| 5 | Linear OOA(8181, 3293, F81, 2, 37) (dual of [(3293, 2), 6505, 38]-NRT-code) | [i] | OOA Folding | |