Information on Result #698645
Linear OA(6491, 4119, F64, 42) (dual of [4119, 4028, 43]-code), using construction X applied to C([0,21]) ⊂ C([0,17]) based on
- linear OA(6485, 4097, F64, 43) (dual of [4097, 4012, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(6469, 4097, F64, 35) (dual of [4097, 4028, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (BCH-bound) [i]
- linear OA(646, 22, F64, 6) (dual of [22, 16, 7]-code or 22-arc in PG(5,64)), using
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- Reed–Solomon code RS(58,64) [i]
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), 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(6491, 2881, F64, 2, 42) (dual of [(2881, 2), 5671, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(6491, 2881, F64, 3, 42) (dual of [(2881, 3), 8552, 43]-NRT-code) | [i] | ||
| 3 | Digital (49, 91, 2881)-net over F64 | [i] | ||