Information on Result #699825
Linear OA(12854, 16390, F128, 27) (dual of [16390, 16336, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,12]) based on
- linear OA(12853, 16385, F128, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(12849, 16385, F128, 25) (dual of [16385, 16336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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(1695, 16390, S16, 27) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3276, 16390, S32, 27) | [i] | ||
| 3 | OA(6463, 16390, S64, 27) | [i] | ||
| 4 | Linear OA(12868, 16540, F128, 27) (dual of [16540, 16472, 28]-code) | [i] | (u, u+v)-Construction | |
| 5 | Linear OA(12870, 16582, F128, 27) (dual of [16582, 16512, 28]-code) | [i] | ||
| 6 | Linear OA(12875, 16773, F128, 27) (dual of [16773, 16698, 28]-code) | [i] | ||
| 7 | Linear OA(12876, 16776, F128, 27) (dual of [16776, 16700, 28]-code) | [i] | ||
| 8 | Linear OOA(12854, 8195, F128, 2, 27) (dual of [(8195, 2), 16336, 28]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(12854, 5463, F128, 3, 27) (dual of [(5463, 3), 16335, 28]-NRT-code) | [i] | ||
| 10 | Linear OOA(12854, 4097, F128, 4, 27) (dual of [(4097, 4), 16334, 28]-NRT-code) | [i] | ||