Information on Result #2267063
Linear OA(3244, 6581, F3, 45) (dual of [6581, 6337, 46]-code), using 2 times code embedding in larger space based on linear OA(3242, 6579, F3, 45) (dual of [6579, 6337, 46]-code), using
- construction X applied to C([0,22]) ⊂ C([0,21]) [i] based on
- linear OA(3241, 6562, F3, 45) (dual of [6562, 6321, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- linear OA(3225, 6562, F3, 43) (dual of [6562, 6337, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(31, 17, F3, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 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(3244, 4154, F3, 2, 45) (dual of [(4154, 2), 8064, 46]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3244, 4154, F3, 3, 45) (dual of [(4154, 3), 12218, 46]-NRT-code) | [i] | ||
| 3 | Linear OOA(3244, 4154, F3, 4, 45) (dual of [(4154, 4), 16372, 46]-NRT-code) | [i] | ||
| 4 | Linear OOA(3244, 4154, F3, 5, 45) (dual of [(4154, 5), 20526, 46]-NRT-code) | [i] | ||
| 5 | Digital (199, 244, 4154)-net over F3 | [i] | ||