Information on Result #698648
Linear OA(6480, 4120, F64, 37) (dual of [4120, 4040, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,14]) based on
- 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(6457, 4097, F64, 29) (dual of [4097, 4040, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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 | Linear OA(8160, 8240, F8, 37) (dual of [8240, 8080, 38]-code) | [i] | Trace Code | |
| 2 | OA(3296, 4120, S32, 37) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(6480, 2618, F64, 2, 37) (dual of [(2618, 2), 5156, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(6480, 2618, F64, 3, 37) (dual of [(2618, 3), 7774, 38]-NRT-code) | [i] | ||
| 5 | Digital (43, 80, 2618)-net over F64 | [i] | ||
| 6 | Linear OOA(6480, 2060, F64, 2, 37) (dual of [(2060, 2), 4040, 38]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(6480, 1373, F64, 3, 37) (dual of [(1373, 3), 4039, 38]-NRT-code) | [i] | ||