Information on Result #678531
Linear OA(4226, 65554, F4, 37) (dual of [65554, 65328, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,17]) based on
- 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(4209, 65537, F4, 35) (dual of [65537, 65328, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,17], and minimum distance d ≥ |{−17,−16,…,17}|+1 = 36 (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(4226, 34370, F4, 2, 37) (dual of [(34370, 2), 68514, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4226, 34370, F4, 3, 37) (dual of [(34370, 3), 102884, 38]-NRT-code) | [i] | ||
| 3 | Digital (189, 226, 34370)-net over F4 | [i] | ||