Information on Result #869116
Linear OOA(3218, 515, F32, 2, 9) (dual of [(515, 2), 1012, 10]-NRT-code), using OOA 2-folding based on linear OA(3218, 1030, F32, 9) (dual of [1030, 1012, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(3217, 1025, F32, 9) (dual of [1025, 1008, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(3213, 1025, F32, 7) (dual of [1025, 1012, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 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(32104, 4194816, F32, 2, 18) (dual of [(4194816, 2), 8389528, 19]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(32109, 4194816, F32, 2, 19) (dual of [(4194816, 2), 8389523, 20]-NRT-code) | [i] | ||
| 3 | OOA(32101, 4194816, S32, 2, 18) | [i] | ||
| 4 | OOA(32106, 4194816, S32, 2, 19) | [i] | ||
| 5 | Digital (9, 18, 515)-net over F32 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |