Information on Result #696481
Linear OA(3282, 1048586, F32, 21) (dual of [1048586, 1048504, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,9]) based on
- linear OA(3281, 1048577, F32, 21) (dual of [1048577, 1048496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3273, 1048577, F32, 19) (dual of [1048577, 1048504, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 328−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(3293, 1048630, F32, 21) (dual of [1048630, 1048537, 22]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(3295, 1048650, F32, 21) (dual of [1048650, 1048555, 22]-code) | [i] | ||
| 3 | Linear OA(3298, 1048681, F32, 21) (dual of [1048681, 1048583, 22]-code) | [i] | ||
| 4 | Linear OA(3299, 1048684, F32, 21) (dual of [1048684, 1048585, 22]-code) | [i] | ||
| 5 | Linear OOA(3282, 667636, F32, 2, 21) (dual of [(667636, 2), 1335190, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (61, 82, 667636)-net over F32 | [i] | ||
| 7 | Linear OOA(3282, 524293, F32, 2, 21) (dual of [(524293, 2), 1048504, 22]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3282, 104858, F32, 21, 21) (dual of [(104858, 21), 2201936, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |