Information on Result #698666
Linear OA(6462, 4126, F64, 27) (dual of [4126, 4064, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,8]) 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(6433, 4097, F64, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(649, 29, F64, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,64)), using
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), using
- Reed–Solomon code RS(55,64) [i]
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), 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(3275, 4126, S32, 27) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6462, 4113, F64, 2, 27) (dual of [(4113, 2), 8164, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6462, 4113, F64, 3, 27) (dual of [(4113, 3), 12277, 28]-NRT-code) | [i] | ||
| 4 | Digital (35, 62, 4113)-net over F64 | [i] | ||
| 5 | Linear OOA(6462, 2063, F64, 2, 27) (dual of [(2063, 2), 4064, 28]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6462, 1375, F64, 3, 27) (dual of [(1375, 3), 4063, 28]-NRT-code) | [i] | ||