Information on Result #699536
Linear OA(8144, 6578, F81, 20) (dual of [6578, 6534, 21]-code), using construction X applied to Ce(19) ⊂ Ce(13) based on
- linear OA(8139, 6561, F81, 20) (dual of [6561, 6522, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8127, 6561, F81, 14) (dual of [6561, 6534, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(815, 17, F81, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,81)), using
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- Reed–Solomon code RS(76,81) [i]
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), 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(8144, 3413, F81, 2, 20) (dual of [(3413, 2), 6782, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8144, 3413, F81, 3, 20) (dual of [(3413, 3), 10195, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(8144, 3413, F81, 4, 20) (dual of [(3413, 4), 13608, 21]-NRT-code) | [i] | ||
| 4 | Digital (24, 44, 3413)-net over F81 | [i] | ||
| 5 | Linear OOA(8144, 3289, F81, 2, 20) (dual of [(3289, 2), 6534, 21]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8144, 2192, F81, 3, 20) (dual of [(2192, 3), 6532, 21]-NRT-code) | [i] | ||
| 7 | Linear OOA(8144, 1644, F81, 4, 20) (dual of [(1644, 4), 6532, 21]-NRT-code) | [i] | ||