Information on Result #682575
Linear OA(5134, 15639, F5, 27) (dual of [15639, 15505, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,12]) based on
- linear OA(5133, 15626, F5, 27) (dual of [15626, 15493, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(5121, 15626, F5, 25) (dual of [15626, 15505, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(51, 13, F5, 1) (dual of [13, 12, 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
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(5134, 13290, F5, 2, 27) (dual of [(13290, 2), 26446, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5134, 13290, F5, 3, 27) (dual of [(13290, 3), 39736, 28]-NRT-code) | [i] | ||
| 3 | Digital (107, 134, 13290)-net over F5 | [i] | ||