Information on Result #878296
Linear OOA(12819, 1048577, F128, 2, 7) (dual of [(1048577, 2), 2097135, 8]-NRT-code), using OOA 2-folding based on linear OA(12819, 2097154, F128, 7) (dual of [2097154, 2097135, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(12819, 2097155, F128, 7) (dual of [2097155, 2097136, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(12819, 2097152, F128, 7) (dual of [2097152, 2097133, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 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
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
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(12822, 1048706, F128, 2, 7) (dual of [(1048706, 2), 2097390, 8]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12823, 1064962, F128, 2, 7) (dual of [(1064962, 2), 2129901, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(12824, 1097733, F128, 2, 7) (dual of [(1097733, 2), 2195442, 8]-NRT-code) | [i] | ||
| 4 | Linear OOA(12872, 5242878, F128, 2, 14) (dual of [(5242878, 2), 10485684, 15]-NRT-code) | [i] | ||
| 5 | Linear OOA(12876, 5242878, F128, 2, 15) (dual of [(5242878, 2), 10485680, 16]-NRT-code) | [i] | ||
| 6 | OOA(12865, 5242878, S128, 2, 14) | [i] | ||
| 7 | OOA(12869, 5242878, S128, 2, 15) | [i] | ||
| 8 | Linear OOA(12833, large, F128, 2, 7) | [i] | Generalized (u, u+v)-Construction for OOAs | |
| 9 | Linear OOA(12819, 1048577, F128, 3, 7) (dual of [(1048577, 3), 3145712, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 10 | Linear OOA(12819, 1048577, F128, 4, 7) (dual of [(1048577, 4), 4194289, 8]-NRT-code) | [i] | ||
| 11 | Digital (12, 19, 1048577)-net over F128 | [i] | ||