Information on Result #698629
Linear OA(6490, 4114, F64, 43) (dual of [4114, 4024, 44]-code), using construction X applied to C([0,21]) ⊂ C([0,18]) 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(6473, 4097, F64, 37) (dual of [4097, 4024, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(645, 17, F64, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,64)), using
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), using
- Reed–Solomon code RS(59,64) [i]
- discarding factors / shortening the dual code based on linear OA(645, 64, F64, 5) (dual of [64, 59, 6]-code or 64-arc in PG(4,64)), 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 | OA(32108, 4114, S32, 43) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6490, 2115, F64, 2, 43) (dual of [(2115, 2), 4140, 44]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6490, 2115, F64, 3, 43) (dual of [(2115, 3), 6255, 44]-NRT-code) | [i] | ||
| 4 | Digital (47, 90, 2115)-net over F64 | [i] | ||
| 5 | Linear OOA(6490, 2057, F64, 2, 43) (dual of [(2057, 2), 4024, 44]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6490, 1371, F64, 3, 43) (dual of [(1371, 3), 4023, 44]-NRT-code) | [i] | ||