Information on Result #698945
Linear OA(6457, 4122, F64, 25) (dual of [4122, 4065, 26]-code), using construction X applied to Ce(24) ⊂ Ce(15) based on
- linear OA(6449, 4096, F64, 25) (dual of [4096, 4047, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(6431, 4096, F64, 16) (dual of [4096, 4065, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(3269, 4122, S32, 25) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(6457, 3728, F64, 2, 25) (dual of [(3728, 2), 7399, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(6457, 3728, F64, 3, 25) (dual of [(3728, 3), 11127, 26]-NRT-code) | [i] | ||
| 4 | Digital (32, 57, 3728)-net over F64 | [i] | ||
| 5 | Linear OOA(6457, 2061, F64, 2, 25) (dual of [(2061, 2), 4065, 26]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(6457, 1374, F64, 3, 25) (dual of [(1374, 3), 4065, 26]-NRT-code) | [i] | ||