Information on Result #869727
Linear OOA(3242, 515, F32, 2, 21) (dual of [(515, 2), 988, 22]-NRT-code), using OOA 2-folding based on linear OA(3242, 1030, F32, 21) (dual of [1030, 988, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(3241, 1025, F32, 21) (dual of [1025, 984, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3237, 1025, F32, 19) (dual of [1025, 988, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(3253, 559, F32, 2, 21) (dual of [(559, 2), 1065, 22]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(3255, 579, F32, 2, 21) (dual of [(579, 2), 1103, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(3257, 591, F32, 2, 21) (dual of [(591, 2), 1125, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(3259, 613, F32, 2, 21) (dual of [(613, 2), 1167, 22]-NRT-code) | [i] | ||
| 5 | Digital (21, 42, 515)-net over F32 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |