Information on Result #699552
Linear OA(8159, 6581, F81, 27) (dual of [6581, 6522, 28]-code), using construction X applied to Ce(26) ⊂ Ce(19) based on
- linear OA(8153, 6561, F81, 27) (dual of [6561, 6508, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(816, 20, F81, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,81)), using
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), using
- Reed–Solomon code RS(75,81) [i]
- discarding factors / shortening the dual code based on linear OA(816, 81, F81, 6) (dual of [81, 75, 7]-code or 81-arc in PG(5,81)), 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 OA(9118, 13162, F9, 27) (dual of [13162, 13044, 28]-code) | [i] | Trace Code | |
| 2 | Linear OOA(8159, 3394, F81, 2, 27) (dual of [(3394, 2), 6729, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8159, 3394, F81, 3, 27) (dual of [(3394, 3), 10123, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(8159, 3394, F81, 4, 27) (dual of [(3394, 4), 13517, 28]-NRT-code) | [i] | ||
| 5 | Digital (32, 59, 3394)-net over F81 | [i] | ||
| 6 | Linear OOA(8159, 3290, F81, 2, 27) (dual of [(3290, 2), 6521, 28]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8159, 1645, F81, 4, 27) (dual of [(1645, 4), 6521, 28]-NRT-code) | [i] | ||