Information on Result #696720
Linear OA(3256, 32776, F32, 19) (dual of [32776, 32720, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,8]) based on
- linear OA(3255, 32769, F32, 19) (dual of [32769, 32714, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(3249, 32769, F32, 17) (dual of [32769, 32720, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 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 OA(3266, 32820, F32, 19) (dual of [32820, 32754, 20]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(3268, 32840, F32, 19) (dual of [32840, 32772, 20]-code) | [i] | ||
| 3 | Linear OA(3271, 32873, F32, 19) (dual of [32873, 32802, 20]-code) | [i] | ||
| 4 | Linear OOA(3256, 17139, F32, 2, 19) (dual of [(17139, 2), 34222, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (37, 56, 17139)-net over F32 | [i] | ||
| 6 | Linear OOA(3256, 16388, F32, 2, 19) (dual of [(16388, 2), 32720, 20]-NRT-code) | [i] | OOA Folding | |