Information on Result #989506
Linear OOA(6442, 1367, F64, 3, 21) (dual of [(1367, 3), 4059, 22]-NRT-code), using OOA 3-folding based on linear OA(6442, 4101, F64, 21) (dual of [4101, 4059, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(6442, 4102, F64, 21) (dual of [4102, 4060, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(6441, 4097, F64, 21) (dual of [4097, 4056, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(6437, 4097, F64, 19) (dual of [4097, 4060, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
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(6453, 1447, F64, 3, 21) (dual of [(1447, 3), 4288, 22]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(6455, 1471, F64, 3, 21) (dual of [(1471, 3), 4358, 22]-NRT-code) | [i] | ||
| 3 | Digital (21, 42, 1367)-net over F64 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |