Information on Result #696624
Linear OA(3232, 1048595, F32, 8) (dual of [1048595, 1048563, 9]-code), using construction X applied to Ce(7) ⊂ Ce(3) based on
- linear OA(3229, 1048576, F32, 8) (dual of [1048576, 1048547, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(323, 19, F32, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,32) or 19-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), 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 OOA(3232, 1048595, F32, 2, 8) (dual of [(1048595, 2), 2097158, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (24, 32, 1048595)-net over F32 | [i] | ||
| 3 | Linear OOA(3232, 524297, F32, 2, 8) (dual of [(524297, 2), 1048562, 9]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3232, 262148, F32, 8, 8) (dual of [(262148, 8), 2097152, 9]-NRT-code) | [i] | OA Folding and Stacking | |