Information on Result #878290
Linear OOA(12813, 8193, F128, 2, 7) (dual of [(8193, 2), 16373, 8]-NRT-code), using OOA 2-folding based on linear OA(12813, 16386, F128, 7) (dual of [16386, 16373, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- 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(12811, 16384, F128, 6) (dual of [16384, 16373, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(12816, 8322, F128, 2, 7) (dual of [(8322, 2), 16628, 8]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12817, 16386, F128, 2, 7) (dual of [(16386, 2), 32755, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(12866, 4202494, F128, 2, 14) (dual of [(4202494, 2), 8404922, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(12870, 4202494, F128, 2, 15) (dual of [(4202494, 2), 8404918, 16]-NRT-code) | [i] | ||
| 5 | OOA(12859, 4202494, S128, 2, 14) | [i] | ||
| 6 | OOA(12863, 4202494, S128, 2, 15) | [i] | ||
| 7 | Linear OOA(12813, 8193, F128, 3, 7) (dual of [(8193, 3), 24566, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 8 | Linear OOA(12813, 8193, F128, 4, 7) (dual of [(8193, 4), 32759, 8]-NRT-code) | [i] | ||
| 9 | Digital (6, 13, 8193)-net over F128 | [i] | ||