Information on Result #699353
Linear OA(8170, 6591, F81, 31) (dual of [6591, 6521, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,10]) based on
- linear OA(8161, 6562, F81, 31) (dual of [6562, 6501, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(8141, 6562, F81, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(819, 29, F81, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,81)), using
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), using
- Reed–Solomon code RS(72,81) [i]
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), 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(8170, 5055, F81, 2, 31) (dual of [(5055, 2), 10040, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8170, 5055, F81, 3, 31) (dual of [(5055, 3), 15095, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(8170, 5055, F81, 4, 31) (dual of [(5055, 4), 20150, 32]-NRT-code) | [i] | ||
| 4 | Digital (39, 70, 5055)-net over F81 | [i] | ||
| 5 | Linear OOA(8170, 3295, F81, 2, 31) (dual of [(3295, 2), 6520, 32]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8170, 2197, F81, 3, 31) (dual of [(2197, 3), 6521, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(8170, 1647, F81, 4, 31) (dual of [(1647, 4), 6518, 32]-NRT-code) | [i] | ||