Information on Result #699829
Linear OA(12838, 16390, F128, 19) (dual of [16390, 16352, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,8]) based on
- linear OA(12837, 16385, F128, 19) (dual of [16385, 16348, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 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(1667, 16390, S16, 19) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3254, 16390, S32, 19) | [i] | ||
| 3 | OA(6445, 16390, S64, 19) | [i] | ||
| 4 | Linear OA(12848, 16540, F128, 19) (dual of [16540, 16492, 20]-code) | [i] | (u, u+v)-Construction | |
| 5 | Linear OA(12853, 16775, F128, 19) (dual of [16775, 16722, 20]-code) | [i] | ||
| 6 | Linear OOA(12838, 8195, F128, 2, 19) (dual of [(8195, 2), 16352, 20]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12838, 5463, F128, 3, 19) (dual of [(5463, 3), 16351, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(12838, 4097, F128, 4, 19) (dual of [(4097, 4), 16350, 20]-NRT-code) | [i] | ||
| 9 | Linear OOA(12838, 1821, F128, 19, 19) (dual of [(1821, 19), 34561, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |