Information on Result #698908
Linear OA(6443, 4116, F64, 19) (dual of [4116, 4073, 20]-code), using construction X applied to Ce(18) ⊂ Ce(11) based on
- linear OA(6437, 4096, F64, 19) (dual of [4096, 4059, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(6423, 4096, F64, 12) (dual of [4096, 4073, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(3252, 4116, S32, 19) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6443, 3295, F64, 2, 19) (dual of [(3295, 2), 6547, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6443, 3295, F64, 3, 19) (dual of [(3295, 3), 9842, 20]-NRT-code) | [i] | ||
| 4 | Digital (24, 43, 3295)-net over F64 | [i] | ||
| 5 | Linear OOA(6443, 2058, F64, 2, 19) (dual of [(2058, 2), 4073, 20]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6443, 1372, F64, 3, 19) (dual of [(1372, 3), 4073, 20]-NRT-code) | [i] | ||