Information on Result #698671
Linear OA(6488, 4132, F64, 39) (dual of [4132, 4044, 40]-code), using construction X applied to C([0,19]) ⊂ C([0,13]) based on
- linear OA(6477, 4097, F64, 39) (dual of [4097, 4020, 40]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,19], and minimum distance d ≥ |{−19,−18,…,19}|+1 = 40 (BCH-bound) [i]
- 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(6411, 35, F64, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,64)), using
- discarding factors / shortening the dual code based on linear OA(6411, 64, F64, 11) (dual of [64, 53, 12]-code or 64-arc in PG(10,64)), using
- Reed–Solomon code RS(53,64) [i]
- discarding factors / shortening the dual code based on linear OA(6411, 64, F64, 11) (dual of [64, 53, 12]-code or 64-arc in PG(10,64)), 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(32106, 4132, S32, 39) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6488, 4089, F64, 2, 39) (dual of [(4089, 2), 8090, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6488, 4089, F64, 3, 39) (dual of [(4089, 3), 12179, 40]-NRT-code) | [i] | ||
| 4 | Digital (49, 88, 4089)-net over F64 | [i] | ||
| 5 | Linear OOA(6488, 2066, F64, 2, 39) (dual of [(2066, 2), 4044, 40]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6488, 1377, F64, 3, 39) (dual of [(1377, 3), 4043, 40]-NRT-code) | [i] | ||