Information on Result #696483
Linear OA(3266, 1048586, F32, 17) (dual of [1048586, 1048520, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,7]) based on
- linear OA(3265, 1048577, F32, 17) (dual of [1048577, 1048512, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(3257, 1048577, F32, 15) (dual of [1048577, 1048520, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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 OA(3275, 1048630, F32, 17) (dual of [1048630, 1048555, 18]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(3277, 1048650, F32, 17) (dual of [1048650, 1048573, 18]-code) | [i] | ||
| 3 | Linear OA(3279, 1048682, F32, 17) (dual of [1048682, 1048603, 18]-code) | [i] | ||
| 4 | Linear OOA(3266, 689790, F32, 2, 17) (dual of [(689790, 2), 1379514, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (49, 66, 689790)-net over F32 | [i] | ||
| 6 | Linear OOA(3266, 524293, F32, 2, 17) (dual of [(524293, 2), 1048520, 18]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3266, 131073, F32, 17, 17) (dual of [(131073, 17), 2228175, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |