Information on Result #699335
Linear OA(8142, 6579, F81, 19) (dual of [6579, 6537, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,6]) based on
- linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(8125, 6562, F81, 13) (dual of [6562, 6537, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [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(8142, 3587, F81, 2, 19) (dual of [(3587, 2), 7132, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8142, 3587, F81, 3, 19) (dual of [(3587, 3), 10719, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(8142, 3587, F81, 4, 19) (dual of [(3587, 4), 14306, 20]-NRT-code) | [i] | ||
| 4 | Digital (23, 42, 3587)-net over F81 | [i] | ||
| 5 | Linear OOA(8142, 3289, F81, 2, 19) (dual of [(3289, 2), 6536, 20]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8142, 2193, F81, 3, 19) (dual of [(2193, 3), 6537, 20]-NRT-code) | [i] | ||
| 7 | Linear OOA(8142, 1644, F81, 4, 19) (dual of [(1644, 4), 6534, 20]-NRT-code) | [i] | ||