Information on Result #696612
Linear OA(3231, 1048590, F32, 8) (dual of [1048590, 1048559, 9]-code), using construction X applied to Ce(7) ⊂ Ce(4) 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(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(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 OOA(3231, 1048590, F32, 2, 8) (dual of [(1048590, 2), 2097149, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (23, 31, 1048590)-net over F32 | [i] | ||
| 3 | Linear OOA(3231, 524295, F32, 2, 8) (dual of [(524295, 2), 1048559, 9]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3231, 262147, F32, 8, 8) (dual of [(262147, 8), 2097145, 9]-NRT-code) | [i] | OA Folding and Stacking | |