Information on Result #698860
Linear OA(6437, 4110, F64, 17) (dual of [4110, 4073, 18]-code), using construction X applied to Ce(16) ⊂ Ce(11) based on
- linear OA(6433, 4096, F64, 17) (dual of [4096, 4063, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(6423, 4096, F64, 12) (dual of [4096, 4073, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(644, 14, F64, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), 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(3245, 4110, S32, 17) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6437, 2198, F64, 2, 17) (dual of [(2198, 2), 4359, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6437, 2198, F64, 3, 17) (dual of [(2198, 3), 6557, 18]-NRT-code) | [i] | ||
| 4 | Digital (20, 37, 2198)-net over F64 | [i] | ||
| 5 | Linear OOA(6437, 2055, F64, 2, 17) (dual of [(2055, 2), 4073, 18]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6437, 1370, F64, 3, 17) (dual of [(1370, 3), 4073, 18]-NRT-code) | [i] | ||