Information on Result #992737
Linear OOA(12862, 699053, F128, 3, 21) (dual of [(699053, 3), 2097097, 22]-NRT-code), using OOA 3-folding based on linear OA(12862, 2097159, F128, 21) (dual of [2097159, 2097097, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(12862, 2097160, F128, 21) (dual of [2097160, 2097098, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(12861, 2097153, F128, 21) (dual of [2097153, 2097092, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(12855, 2097153, F128, 19) (dual of [2097153, 2097098, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,10]) ⊂ C([0,9]) [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(12873, 699203, F128, 3, 21) (dual of [(699203, 3), 2097536, 22]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12875, 699245, F128, 3, 21) (dual of [(699245, 3), 2097660, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(12862, 699053, F128, 4, 21) (dual of [(699053, 4), 2796150, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (41, 62, 699053)-net over F128 | [i] | ||