Information on Result #699655
Linear OA(12856, 2097160, F128, 19) (dual of [2097160, 2097104, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,8]) based on
- 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(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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
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 | OA(1698, 2097160, S16, 19) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3279, 2097160, S32, 19) | [i] | ||
| 3 | OA(6466, 2097160, S64, 19) | [i] | ||
| 4 | Linear OA(12866, 2097310, F128, 19) (dual of [2097310, 2097244, 20]-code) | [i] | (u, u+v)-Construction | |
| 5 | Linear OA(12871, 2097545, F128, 19) (dual of [2097545, 2097474, 20]-code) | [i] | ||
| 6 | Linear OOA(12856, 1048580, F128, 2, 19) (dual of [(1048580, 2), 2097104, 20]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12856, 699053, F128, 3, 19) (dual of [(699053, 3), 2097103, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(12856, 524290, F128, 4, 19) (dual of [(524290, 4), 2097104, 20]-NRT-code) | [i] | ||