Information on Result #878305
Linear OOA(12815, 8193, F128, 2, 8) (dual of [(8193, 2), 16371, 9]-NRT-code), using OOA 2-folding based on linear OA(12815, 16386, F128, 8) (dual of [16386, 16371, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(12815, 16384, F128, 8) (dual of [16384, 16369, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(12813, 16384, F128, 7) (dual of [16384, 16371, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 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(12819, 8322, F128, 2, 8) (dual of [(8322, 2), 16625, 9]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12820, 8343, F128, 2, 8) (dual of [(8343, 2), 16666, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(12876, 4202494, F128, 2, 16) (dual of [(4202494, 2), 8404912, 17]-NRT-code) | [i] | ||
| 4 | OOA(12868, 4202494, S128, 2, 16) | [i] | ||
| 5 | OOA(12871, 4202494, S128, 2, 17) | [i] | ||
| 6 | Linear OOA(12815, 6175, F128, 3, 8) (dual of [(6175, 3), 18510, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(12815, 6175, F128, 4, 8) (dual of [(6175, 4), 24685, 9]-NRT-code) | [i] | ||
| 8 | Digital (7, 15, 6175)-net over F128 | [i] | ||