Information on Result #662686
Linear OA(522, 4808, F5, 5) (dual of [4808, 4786, 6]-code), using generalized (u, u+v)-construction based on
- linear OA(51, 1202, F5, 1) (dual of [1202, 1201, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(51, 1202, F5, 1) (dual of [1202, 1201, 2]-code) (see above)
- linear OA(56, 1202, F5, 2) (dual of [1202, 1196, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(56, 3125, F5, 2) (dual of [3125, 3119, 3]-code), using
- an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(56, 3125, F5, 2) (dual of [3125, 3119, 3]-code), using
- linear OA(514, 1202, F5, 5) (dual of [1202, 1188, 6]-code), using
- trace code [i] based on linear OA(257, 601, F25, 5) (dual of [601, 594, 6]-code), 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 OOA(522, 4808, F5, 2, 5) (dual of [(4808, 2), 9594, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(522, 4808, F5, 3, 5) (dual of [(4808, 3), 14402, 6]-NRT-code) | [i] | ||
| 3 | Digital (17, 22, 4808)-net over F5 | [i] | ||
| 4 | Linear OOA(522, 2404, F5, 2, 5) (dual of [(2404, 2), 4786, 6]-NRT-code) | [i] | OOA Folding | |