Information on Result #678893
Linear OA(4240, 16400, F4, 45) (dual of [16400, 16160, 46]-code), using construction X applied to C([0,22]) ⊂ C([0,21]) based on
- linear OA(4239, 16385, F4, 45) (dual of [16385, 16146, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- linear OA(4225, 16385, F4, 43) (dual of [16385, 16160, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 414−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(41, 15, F4, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 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(4240, 12459, F4, 2, 45) (dual of [(12459, 2), 24678, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4240, 12459, F4, 3, 45) (dual of [(12459, 3), 37137, 46]-NRT-code) | [i] | ||
| 3 | Digital (195, 240, 12459)-net over F4 | [i] | ||