Information on Result #992300
Linear OOA(12817, 5462, F128, 3, 9) (dual of [(5462, 3), 16369, 10]-NRT-code), using OOA 3-folding based on linear OA(12817, 16386, F128, 9) (dual of [16386, 16369, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(12817, 16384, F128, 9) (dual of [16384, 16367, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 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(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(12821, 5591, F128, 3, 9) (dual of [(5591, 3), 16752, 10]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12822, 5612, F128, 3, 9) (dual of [(5612, 3), 16814, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(12823, 10924, F128, 3, 9) (dual of [(10924, 3), 32749, 10]-NRT-code) | [i] | ||
| 4 | OOA(12877, 2801663, S128, 3, 18) | [i] | ||
| 5 | Linear OOA(12817, 5462, F128, 4, 9) (dual of [(5462, 4), 21831, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (8, 17, 5462)-net over F128 | [i] | ||