Information on Result #697111
Linear OA(3214, 1030, F32, 7) (dual of [1030, 1016, 8]-code), using construction X applied to C([0,3]) ⊂ C([0,2]) based on
- 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(329, 1025, F32, 5) (dual of [1025, 1016, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (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(824, 1030, S8, 7) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(1618, 1030, S16, 7) | [i] | ||
| 3 | Linear OA(3218, 2055, F32, 7) (dual of [2055, 2037, 8]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OOA(3214, 687, F32, 2, 7) (dual of [(687, 2), 1360, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (7, 14, 687)-net over F32 | [i] | ||
| 6 | Linear OOA(3214, 515, F32, 2, 7) (dual of [(515, 2), 1016, 8]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3214, 343, F32, 7, 7) (dual of [(343, 7), 2387, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |