Information on Result #698637
Linear OA(6458, 4114, F64, 27) (dual of [4114, 4056, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,10]) 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(6441, 4097, F64, 21) (dual of [4097, 4056, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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 | OA(3270, 4114, S32, 27) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6458, 2109, F64, 2, 27) (dual of [(2109, 2), 4160, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6458, 2109, F64, 3, 27) (dual of [(2109, 3), 6269, 28]-NRT-code) | [i] | ||
| 4 | Digital (31, 58, 2109)-net over F64 | [i] | ||
| 5 | Linear OOA(6458, 2057, F64, 2, 27) (dual of [(2057, 2), 4056, 28]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6458, 1371, F64, 3, 27) (dual of [(1371, 3), 4055, 28]-NRT-code) | [i] | ||