Information on Result #698879
Linear OA(6444, 4113, F64, 20) (dual of [4113, 4069, 21]-code), using construction X applied to Ce(19) ⊂ Ce(13) based on
- linear OA(6439, 4096, F64, 20) (dual of [4096, 4057, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(6427, 4096, F64, 14) (dual of [4096, 4069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(3253, 4113, S32, 20) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6444, 2467, F64, 2, 20) (dual of [(2467, 2), 4890, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6444, 2467, F64, 3, 20) (dual of [(2467, 3), 7357, 21]-NRT-code) | [i] | ||
| 4 | Digital (24, 44, 2467)-net over F64 | [i] | ||
| 5 | Linear OOA(6444, 2056, F64, 2, 20) (dual of [(2056, 2), 4068, 21]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6444, 1371, F64, 3, 20) (dual of [(1371, 3), 4069, 21]-NRT-code) | [i] | ||