Information on Result #697099
Linear OA(3262, 1030, F32, 31) (dual of [1030, 968, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,14]) based on
- linear OA(3261, 1025, F32, 31) (dual of [1025, 964, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(3257, 1025, F32, 29) (dual of [1025, 968, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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 | OA(8104, 1030, S8, 31) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(1678, 1030, S16, 31) | [i] | ||
| 3 | Linear OA(3280, 1094, F32, 31) (dual of [1094, 1014, 32]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OA(3282, 1106, F32, 31) (dual of [1106, 1024, 32]-code) | [i] | ||
| 5 | Linear OA(3284, 1128, F32, 31) (dual of [1128, 1044, 32]-code) | [i] | ||
| 6 | Linear OA(3286, 1134, F32, 31) (dual of [1134, 1048, 32]-code) | [i] | ||
| 7 | Linear OA(3288, 1150, F32, 31) (dual of [1150, 1062, 32]-code) | [i] | ||
| 8 | Linear OOA(3262, 539, F32, 2, 31) (dual of [(539, 2), 1016, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 9 | Digital (31, 62, 539)-net over F32 | [i] | ||
| 10 | Linear OOA(3262, 515, F32, 2, 31) (dual of [(515, 2), 968, 32]-NRT-code) | [i] | OOA Folding | |