Information on Result #678525
Linear OA(4242, 65554, F4, 39) (dual of [65554, 65312, 40]-code), using construction X applied to C([0,20]) ⊂ C([0,18]) based on
- linear OA(4241, 65537, F4, 41) (dual of [65537, 65296, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(4225, 65537, F4, 37) (dual of [65537, 65312, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(41, 17, F4, 1) (dual of [17, 16, 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(4242, 40738, F4, 2, 39) (dual of [(40738, 2), 81234, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4242, 40738, F4, 3, 39) (dual of [(40738, 3), 121972, 40]-NRT-code) | [i] | ||
| 3 | Digital (203, 242, 40738)-net over F4 | [i] | ||