Information on Result #679409
Linear OA(4134, 4110, F4, 29) (dual of [4110, 3976, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,13]) based on
- linear OA(4133, 4097, F4, 29) (dual of [4097, 3964, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(4121, 4097, F4, 27) (dual of [4097, 3976, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(41, 13, F4, 1) (dual of [13, 12, 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(4134, 3344, F4, 2, 29) (dual of [(3344, 2), 6554, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4134, 3344, F4, 3, 29) (dual of [(3344, 3), 9898, 30]-NRT-code) | [i] | ||
| 3 | Digital (105, 134, 3344)-net over F4 | [i] | ||