Information on Result #696598
Linear OA(3283, 1048590, F32, 21) (dual of [1048590, 1048507, 22]-code), using construction X applied to Ce(20) ⊂ Ce(17) based on
- linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(3269, 1048576, F32, 18) (dual of [1048576, 1048507, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(322, 14, F32, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), 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(3299, 1048685, F32, 21) (dual of [1048685, 1048586, 22]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(3283, 801234, F32, 2, 21) (dual of [(801234, 2), 1602385, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (62, 83, 801234)-net over F32 | [i] | ||
| 4 | Linear OOA(3283, 524295, F32, 2, 21) (dual of [(524295, 2), 1048507, 22]-NRT-code) | [i] | OOA Folding | |