Information on Result #698953
Linear OA(6488, 4125, F64, 40) (dual of [4125, 4037, 41]-code), using construction X applied to Ce(39) ⊂ Ce(29) based on
- linear OA(6479, 4096, F64, 40) (dual of [4096, 4017, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(6459, 4096, F64, 30) (dual of [4096, 4037, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(649, 29, F64, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,64)), using
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), using
- Reed–Solomon code RS(55,64) [i]
- discarding factors / shortening the dual code based on linear OA(649, 64, F64, 9) (dual of [64, 55, 10]-code or 64-arc in PG(8,64)), 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, 4125, S32, 40) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6488, 3238, F64, 2, 40) (dual of [(3238, 2), 6388, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6488, 3238, F64, 3, 40) (dual of [(3238, 3), 9626, 41]-NRT-code) | [i] | ||
| 4 | Digital (48, 88, 3238)-net over F64 | [i] | ||
| 5 | Linear OOA(6488, 2062, F64, 2, 40) (dual of [(2062, 2), 4036, 41]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6488, 1375, F64, 3, 40) (dual of [(1375, 3), 4037, 41]-NRT-code) | [i] | ||