Information on Result #699823
Linear OA(12862, 16390, F128, 31) (dual of [16390, 16328, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,14]) based on
- linear OA(12861, 16385, F128, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(12857, 16385, F128, 29) (dual of [16385, 16328, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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(16109, 16390, S16, 31) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3287, 16390, S32, 31) | [i] | ||
| 3 | OA(6473, 16390, S64, 31) | [i] | ||
| 4 | Linear OA(12878, 16540, F128, 31) (dual of [16540, 16462, 32]-code) | [i] | (u, u+v)-Construction | |
| 5 | Linear OOA(12862, 8195, F128, 2, 31) (dual of [(8195, 2), 16328, 32]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(12862, 5463, F128, 3, 31) (dual of [(5463, 3), 16327, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(12862, 4097, F128, 4, 31) (dual of [(4097, 4), 16326, 32]-NRT-code) | [i] | ||