Information on Result #696568
Linear OA(3225, 1048580, F32, 7) (dual of [1048580, 1048555, 8]-code), using construction X applied to Ce(6) ⊂ Ce(5) based on
- linear OA(3225, 1048576, F32, 7) (dual of [1048576, 1048551, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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(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(3228, 1048614, F32, 7) (dual of [1048614, 1048586, 8]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(3229, 1049605, F32, 7) (dual of [1049605, 1049576, 8]-code) | [i] | ||
| 3 | Linear OA(3230, 1051716, F32, 7) (dual of [1051716, 1051686, 8]-code) | [i] | ||
| 4 | Linear OOA(3225, 1048580, F32, 2, 7) (dual of [(1048580, 2), 2097135, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (18, 25, 1048580)-net over F32 | [i] | ||
| 6 | Linear OOA(3225, 524290, F32, 2, 7) (dual of [(524290, 2), 1048555, 8]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3225, 349526, F32, 7, 7) (dual of [(349526, 7), 2446657, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |