Information on Result #698869
Linear OA(6484, 4113, F64, 40) (dual of [4113, 4029, 41]-code), using construction X applied to Ce(39) ⊂ Ce(33) 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(6467, 4096, F64, 34) (dual of [4096, 4029, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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 | Linear OA(8168, 8226, F8, 40) (dual of [8226, 8058, 41]-code) | [i] | Trace Code | |
| 2 | OA(32101, 4113, S32, 40) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(6484, 2084, F64, 2, 40) (dual of [(2084, 2), 4084, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(6484, 2084, F64, 3, 40) (dual of [(2084, 3), 6168, 41]-NRT-code) | [i] | ||
| 5 | Digital (44, 84, 2084)-net over F64 | [i] | ||
| 6 | Linear OOA(6484, 2056, F64, 2, 40) (dual of [(2056, 2), 4028, 41]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(6484, 1371, F64, 3, 40) (dual of [(1371, 3), 4029, 41]-NRT-code) | [i] | ||