Information on Result #992784
Linear OOA(12864, 699051, F128, 3, 22) (dual of [(699051, 3), 2097089, 23]-NRT-code), using OOA 3-folding based on linear OA(12864, 2097153, F128, 22) (dual of [2097153, 2097089, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12864, 2097155, F128, 22) (dual of [2097155, 2097091, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12861, 2097152, F128, 21) (dual of [2097152, 2097091, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(21) ⊂ Ce(20) [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(12875, 699180, F128, 3, 22) (dual of [(699180, 3), 2097465, 23]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12876, 699201, F128, 3, 22) (dual of [(699201, 3), 2097527, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(12878, 699243, F128, 3, 22) (dual of [(699243, 3), 2097651, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(12864, 699051, F128, 4, 22) (dual of [(699051, 4), 2796140, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (42, 64, 699051)-net over F128 | [i] | ||