Information on Result #989288
Linear OOA(6431, 1366, F64, 3, 16) (dual of [(1366, 3), 4067, 17]-NRT-code), using OOA 3-folding based on linear OA(6431, 4098, F64, 16) (dual of [4098, 4067, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- 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(6429, 4096, F64, 15) (dual of [4096, 4067, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(6439, 1431, F64, 3, 16) (dual of [(1431, 3), 4254, 17]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(6440, 1446, F64, 3, 16) (dual of [(1446, 3), 4298, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(6442, 1470, F64, 3, 16) (dual of [(1470, 3), 4368, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(6443, 1496, F64, 3, 16) (dual of [(1496, 3), 4445, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(6444, 1511, F64, 3, 16) (dual of [(1511, 3), 4489, 17]-NRT-code) | [i] | ||
| 6 | Digital (15, 31, 1366)-net over F64 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |