Information on Result #699832
Linear OA(12826, 16390, F128, 13) (dual of [16390, 16364, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,5]) based on
- linear OA(12825, 16385, F128, 13) (dual of [16385, 16360, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(12821, 16385, F128, 11) (dual of [16385, 16364, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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(1646, 16390, S16, 13) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(6431, 16390, S64, 13) | [i] | ||
| 3 | Linear OA(12833, 16540, F128, 13) (dual of [16540, 16507, 14]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OOA(12826, 8195, F128, 2, 13) (dual of [(8195, 2), 16364, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(12826, 5463, F128, 3, 13) (dual of [(5463, 3), 16363, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(12826, 4097, F128, 4, 13) (dual of [(4097, 4), 16362, 14]-NRT-code) | [i] | ||
| 7 | Linear OOA(12826, 2731, F128, 13, 13) (dual of [(2731, 13), 35477, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |