Information on Result #878312
Linear OOA(12822, 1048577, F128, 2, 8) (dual of [(1048577, 2), 2097132, 9]-NRT-code), using OOA 2-folding based on linear OA(12822, 2097154, F128, 8) (dual of [2097154, 2097132, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(12822, 2097155, F128, 8) (dual of [2097155, 2097133, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- 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(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(7) ⊂ Ce(6) [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(12826, 1048706, F128, 2, 8) (dual of [(1048706, 2), 2097386, 9]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12827, 1048727, F128, 2, 8) (dual of [(1048727, 2), 2097427, 9]-NRT-code) | [i] | ||
| 3 | OOA(12875, 5242878, S128, 2, 16) | [i] | ||
| 4 | OOA(12878, 5242878, S128, 2, 17) | [i] | ||
| 5 | Linear OOA(12822, 1048577, F128, 3, 8) (dual of [(1048577, 3), 3145709, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(12822, 1048577, F128, 4, 8) (dual of [(1048577, 4), 4194286, 9]-NRT-code) | [i] | ||
| 7 | Digital (14, 22, 1048577)-net over F128 | [i] | ||