Information on Result #699557
Linear OA(8149, 6581, F81, 22) (dual of [6581, 6532, 23]-code), using construction X applied to Ce(21) ⊂ Ce(14) based on
- linear OA(8143, 6561, F81, 22) (dual of [6561, 6518, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(8129, 6561, F81, 15) (dual of [6561, 6532, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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 OOA(8149, 3941, F81, 2, 22) (dual of [(3941, 2), 7833, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8149, 3941, F81, 3, 22) (dual of [(3941, 3), 11774, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(8149, 3941, F81, 4, 22) (dual of [(3941, 4), 15715, 23]-NRT-code) | [i] | ||
| 4 | Digital (27, 49, 3941)-net over F81 | [i] | ||
| 5 | Linear OOA(8149, 3290, F81, 2, 22) (dual of [(3290, 2), 6531, 23]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8149, 2193, F81, 3, 22) (dual of [(2193, 3), 6530, 23]-NRT-code) | [i] | ||
| 7 | Linear OOA(8149, 1645, F81, 4, 22) (dual of [(1645, 4), 6531, 23]-NRT-code) | [i] | ||