Information on Result #697509
Linear OA(3279, 1040, F32, 39) (dual of [1040, 961, 40]-code), using construction X applied to Ce(38) ⊂ Ce(32) based on
- linear OA(3274, 1024, F32, 39) (dual of [1024, 950, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(3263, 1024, F32, 33) (dual of [1024, 961, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(325, 16, F32, 5) (dual of [16, 11, 6]-code or 16-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), 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 | OA(1699, 1040, S16, 39) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(3279, 687, F32, 2, 39) (dual of [(687, 2), 1295, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (40, 79, 687)-net over F32 | [i] | ||
| 4 | Linear OOA(3279, 520, F32, 2, 39) (dual of [(520, 2), 961, 40]-NRT-code) | [i] | OOA Folding | |