Information on Result #698868
Linear OA(6488, 4113, F64, 42) (dual of [4113, 4025, 43]-code), using construction X applied to Ce(41) ⊂ Ce(35) based on
- linear OA(6483, 4096, F64, 42) (dual of [4096, 4013, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(6471, 4096, F64, 36) (dual of [4096, 4025, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [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(32106, 4113, S32, 42) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6488, 2104, F64, 2, 42) (dual of [(2104, 2), 4120, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6488, 2104, F64, 3, 42) (dual of [(2104, 3), 6224, 43]-NRT-code) | [i] | ||
| 4 | Digital (46, 88, 2104)-net over F64 | [i] | ||
| 5 | Linear OOA(6488, 2056, F64, 2, 42) (dual of [(2056, 2), 4024, 43]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6488, 1371, F64, 3, 42) (dual of [(1371, 3), 4025, 43]-NRT-code) | [i] | ||