Information on Result #873777
Linear OOA(6418, 2051, F64, 2, 9) (dual of [(2051, 2), 4084, 10]-NRT-code), using OOA 2-folding based on linear OA(6418, 4102, F64, 9) (dual of [4102, 4084, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(6417, 4097, F64, 9) (dual of [4097, 4080, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(6413, 4097, F64, 7) (dual of [4097, 4084, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 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(6487, 4196352, F64, 2, 18) (dual of [(4196352, 2), 8392617, 19]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(6491, 4196352, F64, 2, 19) (dual of [(4196352, 2), 8392613, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(6418, 2051, F64, 3, 9) (dual of [(2051, 3), 6135, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (9, 18, 2051)-net over F64 | [i] | ||