Information on Result #698014
Linear OA(4942, 5764811, F49, 11) (dual of [5764811, 5764769, 12]-code), using construction X applied to C([0,5]) ⊂ C([0,4]) based on
- linear OA(4941, 5764802, F49, 11) (dual of [5764802, 5764761, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(4933, 5764802, F49, 9) (dual of [5764802, 5764769, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 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 | Linear OA(4947, 5764861, F49, 11) (dual of [5764861, 5764814, 12]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(4949, 5767164, F49, 11) (dual of [5767164, 5767115, 12]-code) | [i] | ||
| 3 | Linear OOA(4942, 4328047, F49, 2, 11) (dual of [(4328047, 2), 8656052, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(4942, 4328047, F49, 3, 11) (dual of [(4328047, 3), 12984099, 12]-NRT-code) | [i] | ||
| 5 | Digital (31, 42, 4328047)-net over F49 | [i] | ||
| 6 | Linear OOA(4942, 2882405, F49, 2, 11) (dual of [(2882405, 2), 5764768, 12]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4942, 1921603, F49, 3, 11) (dual of [(1921603, 3), 5764767, 12]-NRT-code) | [i] | ||
| 8 | Linear OOA(4942, 1152962, F49, 11, 11) (dual of [(1152962, 11), 12682540, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |