Information on Result #698810
Linear OA(6419, 4104, F64, 9) (dual of [4104, 4085, 10]-code), using construction X applied to Ce(8) ⊂ Ce(5) based on
- linear OA(6417, 4096, F64, 9) (dual of [4096, 4079, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(6411, 4096, F64, 6) (dual of [4096, 4085, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(642, 8, F64, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), 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(3223, 4104, S32, 9) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6419, 2364, F64, 2, 9) (dual of [(2364, 2), 4709, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6419, 2364, F64, 3, 9) (dual of [(2364, 3), 7073, 10]-NRT-code) | [i] | ||
| 4 | Digital (10, 19, 2364)-net over F64 | [i] | ||
| 5 | Linear OOA(6419, 2052, F64, 2, 9) (dual of [(2052, 2), 4085, 10]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6419, 1368, F64, 3, 9) (dual of [(1368, 3), 4085, 10]-NRT-code) | [i] | ||