Information on Result #696571
Linear OA(3217, 1048580, F32, 5) (dual of [1048580, 1048563, 6]-code), using construction X applied to Ce(4) ⊂ Ce(3) based on
- 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(3213, 1048576, F32, 4) (dual of [1048576, 1048563, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(3219, 1048613, F32, 5) (dual of [1048613, 1048594, 6]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(3220, 1049637, F32, 5) (dual of [1049637, 1049617, 6]-code) | [i] | ||
| 3 | Linear OOA(3217, 1048580, F32, 2, 5) (dual of [(1048580, 2), 2097143, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (12, 17, 1048580)-net over F32 | [i] | ||
| 5 | Linear OOA(3217, 524290, F32, 2, 5) (dual of [(524290, 2), 1048563, 6]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(3217, 524289, F32, 5, 5) (dual of [(524289, 5), 2621428, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |