Information on Result #698630
Linear OA(6486, 4114, F64, 41) (dual of [4114, 4028, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,17]) based on
- linear OA(6481, 4097, F64, 41) (dual of [4097, 4016, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (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(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 | Linear OA(8172, 8228, F8, 41) (dual of [8228, 8056, 42]-code) | [i] | Trace Code | |
| 2 | OA(32104, 4114, S32, 41) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(6486, 2093, F64, 2, 41) (dual of [(2093, 2), 4100, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(6486, 2093, F64, 3, 41) (dual of [(2093, 3), 6193, 42]-NRT-code) | [i] | ||
| 5 | Digital (45, 86, 2093)-net over F64 | [i] | ||
| 6 | Linear OOA(6486, 2057, F64, 2, 41) (dual of [(2057, 2), 4028, 42]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(6486, 1371, F64, 3, 41) (dual of [(1371, 3), 4027, 42]-NRT-code) | [i] | ||