Information on Result #698653
Linear OA(6460, 4120, F64, 27) (dual of [4120, 4060, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,9]) based on
- linear OA(6453, 4097, F64, 27) (dual of [4097, 4044, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(6437, 4097, F64, 19) (dual of [4097, 4060, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(647, 23, F64, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,64)), using
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), using
- Reed–Solomon code RS(57,64) [i]
- discarding factors / shortening the dual code based on linear OA(647, 64, F64, 7) (dual of [64, 57, 8]-code or 64-arc in PG(6,64)), 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(3272, 4120, S32, 27) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6460, 2945, F64, 2, 27) (dual of [(2945, 2), 5830, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6460, 2945, F64, 3, 27) (dual of [(2945, 3), 8775, 28]-NRT-code) | [i] | ||
| 4 | Digital (33, 60, 2945)-net over F64 | [i] | ||
| 5 | Linear OOA(6460, 2060, F64, 2, 27) (dual of [(2060, 2), 4060, 28]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6460, 1373, F64, 3, 27) (dual of [(1373, 3), 4059, 28]-NRT-code) | [i] | ||