Information on Result #696478
Linear OA(32106, 1048586, F32, 27) (dual of [1048586, 1048480, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,12]) based on
- linear OA(32105, 1048577, F32, 27) (dual of [1048577, 1048472, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(3297, 1048577, F32, 25) (dual of [1048577, 1048480, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(321, 9, F32, 1) (dual of [9, 8, 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(32106, 688472, F32, 2, 27) (dual of [(688472, 2), 1376838, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (79, 106, 688472)-net over F32 | [i] | ||
| 3 | Linear OOA(32106, 524293, F32, 2, 27) (dual of [(524293, 2), 1048480, 28]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(32106, 80660, F32, 27, 27) (dual of [(80660, 27), 2177714, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |