Information on Result #877214
Linear OOA(8163, 3287, F81, 2, 30) (dual of [(3287, 2), 6511, 31]-NRT-code), using OOA 2-folding based on linear OA(8163, 6574, F81, 30) (dual of [6574, 6511, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(8163, 6575, F81, 30) (dual of [6575, 6512, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] 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(8149, 6561, F81, 25) (dual of [6561, 6512, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(814, 14, F81, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,81)), using
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), using
- Reed–Solomon code RS(77,81) [i]
- discarding factors / shortening the dual code based on linear OA(814, 81, F81, 4) (dual of [81, 77, 5]-code or 81-arc in PG(3,81)), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
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, 2787, F81, 3, 30) (dual of [(2787, 3), 8298, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8163, 2787, F81, 4, 30) (dual of [(2787, 4), 11085, 31]-NRT-code) | [i] | ||
| 3 | Digital (33, 63, 2787)-net over F81 | [i] | ||