Information on Result #873758
Linear OOA(6415, 2049, F64, 2, 8) (dual of [(2049, 2), 4083, 9]-NRT-code), using OOA 2-folding based on linear OA(6415, 4098, F64, 8) (dual of [4098, 4083, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(6415, 4096, F64, 8) (dual of [4096, 4081, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(6413, 4096, F64, 7) (dual of [4096, 4083, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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 | Linear OOA(6419, 2114, F64, 2, 8) (dual of [(2114, 2), 4209, 9]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(6420, 2129, F64, 2, 8) (dual of [(2129, 2), 4238, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(6476, 4196350, F64, 2, 16) (dual of [(4196350, 2), 8392624, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(6480, 4196350, F64, 2, 17) (dual of [(4196350, 2), 8392620, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(6415, 2049, F64, 3, 8) (dual of [(2049, 3), 6132, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (7, 15, 2049)-net over F64 | [i] | ||