Information on Result #992687
Linear OOA(12858, 699051, F128, 3, 20) (dual of [(699051, 3), 2097095, 21]-NRT-code), using OOA 3-folding based on linear OA(12858, 2097153, F128, 20) (dual of [2097153, 2097095, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(12858, 2097155, F128, 20) (dual of [2097155, 2097097, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(12855, 2097152, F128, 19) (dual of [2097152, 2097097, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(19) ⊂ Ce(18) [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(12868, 699180, F128, 3, 20) (dual of [(699180, 3), 2097472, 21]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12869, 699201, F128, 3, 20) (dual of [(699201, 3), 2097534, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(12871, 699243, F128, 3, 20) (dual of [(699243, 3), 2097658, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(12873, 699309, F128, 3, 20) (dual of [(699309, 3), 2097854, 21]-NRT-code) | [i] | ||
| 5 | Linear OOA(12874, 699330, F128, 3, 20) (dual of [(699330, 3), 2097916, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(12875, 699351, F128, 3, 20) (dual of [(699351, 3), 2097978, 21]-NRT-code) | [i] | ||
| 7 | Linear OOA(12876, 699372, F128, 3, 20) (dual of [(699372, 3), 2098040, 21]-NRT-code) | [i] | ||
| 8 | Linear OOA(12876, 699438, F128, 3, 20) (dual of [(699438, 3), 2098238, 21]-NRT-code) | [i] | ||
| 9 | Linear OOA(12858, 699051, F128, 4, 20) (dual of [(699051, 4), 2796146, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 10 | Digital (38, 58, 699051)-net over F128 | [i] | ||