Information on Result #991454
Linear OOA(8145, 2189, F81, 3, 22) (dual of [(2189, 3), 6522, 23]-NRT-code), using OOA 3-folding based on linear OA(8145, 6567, F81, 22) (dual of [6567, 6522, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(8145, 6569, F81, 22) (dual of [6569, 6524, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [i] 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(8137, 6561, F81, 19) (dual of [6561, 6524, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(812, 8, F81, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,81)), using
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- Reed–Solomon code RS(79,81) [i]
- discarding factors / shortening the dual code based on linear OA(812, 81, F81, 2) (dual of [81, 79, 3]-code or 81-arc in PG(1,81)), using
- construction X applied to Ce(21) ⊂ Ce(18) [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(8145, 2189, F81, 4, 22) (dual of [(2189, 4), 8711, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (23, 45, 2189)-net over F81 | [i] | ||