Information on Result #698910
Linear OA(6439, 4116, F64, 17) (dual of [4116, 4077, 18]-code), using construction X applied to Ce(16) ⊂ Ce(9) based on
- linear OA(6433, 4096, F64, 17) (dual of [4096, 4063, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(6419, 4096, F64, 10) (dual of [4096, 4077, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(646, 20, F64, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,64)), using
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- Reed–Solomon code RS(58,64) [i]
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), 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(3247, 4116, S32, 17) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6439, 3831, F64, 2, 17) (dual of [(3831, 2), 7623, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6439, 3831, F64, 3, 17) (dual of [(3831, 3), 11454, 18]-NRT-code) | [i] | ||
| 4 | Digital (22, 39, 3831)-net over F64 | [i] | ||
| 5 | Linear OOA(6439, 2058, F64, 2, 17) (dual of [(2058, 2), 4077, 18]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6439, 1372, F64, 3, 17) (dual of [(1372, 3), 4077, 18]-NRT-code) | [i] | ||