Information on Result #698965
Linear OA(6489, 4128, F64, 40) (dual of [4128, 4039, 41]-code), using construction X applied to Ce(39) ⊂ Ce(28) 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(6457, 4096, F64, 29) (dual of [4096, 4039, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(6410, 32, F64, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,64)), using
- discarding factors / shortening the dual code based on linear OA(6410, 64, F64, 10) (dual of [64, 54, 11]-code or 64-arc in PG(9,64)), using
- Reed–Solomon code RS(54,64) [i]
- discarding factors / shortening the dual code based on linear OA(6410, 64, F64, 10) (dual of [64, 54, 11]-code or 64-arc in PG(9,64)), 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(32107, 4128, S32, 40) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6489, 3614, F64, 2, 40) (dual of [(3614, 2), 7139, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6489, 3614, F64, 3, 40) (dual of [(3614, 3), 10753, 41]-NRT-code) | [i] | ||
| 4 | Digital (49, 89, 3614)-net over F64 | [i] | ||
| 5 | Linear OOA(6489, 2064, F64, 2, 40) (dual of [(2064, 2), 4039, 41]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6489, 1376, F64, 3, 40) (dual of [(1376, 3), 4039, 41]-NRT-code) | [i] | ||