Information on Result #698929
Linear OA(6489, 4122, F64, 41) (dual of [4122, 4033, 42]-code), using construction X applied to Ce(40) ⊂ Ce(31) based on
- linear OA(6481, 4096, F64, 41) (dual of [4096, 4015, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(6463, 4096, F64, 32) (dual of [4096, 4033, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(648, 26, F64, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,64)), using
- discarding factors / shortening the dual code based on linear OA(648, 64, F64, 8) (dual of [64, 56, 9]-code or 64-arc in PG(7,64)), using
- Reed–Solomon code RS(56,64) [i]
- discarding factors / shortening the dual code based on linear OA(648, 64, F64, 8) (dual of [64, 56, 9]-code or 64-arc in PG(7,64)), 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, 4122, S32, 41) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6489, 2889, F64, 2, 41) (dual of [(2889, 2), 5689, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6489, 2889, F64, 3, 41) (dual of [(2889, 3), 8578, 42]-NRT-code) | [i] | ||
| 4 | Digital (48, 89, 2889)-net over F64 | [i] | ||
| 5 | Linear OOA(6489, 2061, F64, 2, 41) (dual of [(2061, 2), 4033, 42]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6489, 1374, F64, 3, 41) (dual of [(1374, 3), 4033, 42]-NRT-code) | [i] | ||