Information on Result #696569
Linear OA(3221, 1048580, F32, 6) (dual of [1048580, 1048559, 7]-code), using construction X applied to Ce(5) ⊂ Ce(4) based on
- linear OA(3221, 1048576, F32, 6) (dual of [1048576, 1048555, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(3217, 1048576, F32, 5) (dual of [1048576, 1048559, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(320, 4, F32, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-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(3224, 1048614, F32, 6) (dual of [1048614, 1048590, 7]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(3225, 1049605, F32, 6) (dual of [1049605, 1049580, 7]-code) | [i] | ||
| 3 | Linear OOA(3221, 1048580, F32, 2, 6) (dual of [(1048580, 2), 2097139, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (15, 21, 1048580)-net over F32 | [i] | ||
| 5 | Linear OOA(3221, 524290, F32, 2, 6) (dual of [(524290, 2), 1048559, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(3221, 349526, F32, 6, 6) (dual of [(349526, 6), 2097135, 7]-NRT-code) | [i] | OA Folding and Stacking | |