Information on Result #698939
Linear OA(6469, 4122, F64, 31) (dual of [4122, 4053, 32]-code), using construction X applied to Ce(30) ⊂ Ce(21) based on
- linear OA(6461, 4096, F64, 31) (dual of [4096, 4035, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(3283, 4122, S32, 31) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6469, 3170, F64, 2, 31) (dual of [(3170, 2), 6271, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6469, 3170, F64, 3, 31) (dual of [(3170, 3), 9441, 32]-NRT-code) | [i] | ||
| 4 | Digital (38, 69, 3170)-net over F64 | [i] | ||
| 5 | Linear OOA(6469, 2061, F64, 2, 31) (dual of [(2061, 2), 4053, 32]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6469, 1374, F64, 3, 31) (dual of [(1374, 3), 4053, 32]-NRT-code) | [i] | ||