Information on Result #699587
Linear OA(8163, 6587, F81, 28) (dual of [6587, 6524, 29]-code), using construction X applied to Ce(27) ⊂ Ce(18) based on
- 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(8137, 6561, F81, 19) (dual of [6561, 6524, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(8163, 4678, F81, 2, 28) (dual of [(4678, 2), 9293, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8163, 4678, F81, 3, 28) (dual of [(4678, 3), 13971, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(8163, 4678, F81, 4, 28) (dual of [(4678, 4), 18649, 29]-NRT-code) | [i] | ||
| 4 | Digital (35, 63, 4678)-net over F81 | [i] | ||
| 5 | Linear OOA(8163, 3293, F81, 2, 28) (dual of [(3293, 2), 6523, 29]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8163, 2195, F81, 3, 28) (dual of [(2195, 3), 6522, 29]-NRT-code) | [i] | ||