Information on Result #698906
Linear OA(6447, 4116, F64, 21) (dual of [4116, 4069, 22]-code), using construction X applied to Ce(20) ⊂ Ce(13) based on
- linear OA(6441, 4096, F64, 21) (dual of [4096, 4055, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(6427, 4096, F64, 14) (dual of [4096, 4069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(646, 20, F64, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,64)), using
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), using
- Reed–Solomon code RS(58,64) [i]
- discarding factors / shortening the dual code based on linear OA(646, 64, F64, 6) (dual of [64, 58, 7]-code or 64-arc in PG(5,64)), 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(3257, 4116, S32, 21) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6447, 2961, F64, 2, 21) (dual of [(2961, 2), 5875, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6447, 2961, F64, 3, 21) (dual of [(2961, 3), 8836, 22]-NRT-code) | [i] | ||
| 4 | Digital (26, 47, 2961)-net over F64 | [i] | ||
| 5 | Linear OOA(6447, 2058, F64, 2, 21) (dual of [(2058, 2), 4069, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6447, 1372, F64, 3, 21) (dual of [(1372, 3), 4069, 22]-NRT-code) | [i] | ||