Information on Result #696600
Linear OA(3275, 1048590, F32, 19) (dual of [1048590, 1048515, 20]-code), using construction X applied to Ce(18) ⊂ Ce(15) based on
- linear OA(3273, 1048576, F32, 19) (dual of [1048576, 1048503, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3261, 1048576, F32, 16) (dual of [1048576, 1048515, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(3275, 824914, F32, 2, 19) (dual of [(824914, 2), 1649753, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (56, 75, 824914)-net over F32 | [i] | ||
| 3 | Linear OOA(3275, 524295, F32, 2, 19) (dual of [(524295, 2), 1048515, 20]-NRT-code) | [i] | OOA Folding | |