Information on Result #697466
Linear OA(3276, 1037, F32, 38) (dual of [1037, 961, 39]-code), using construction X applied to Ce(37) ⊂ Ce(32) based on
- linear OA(3272, 1024, F32, 38) (dual of [1024, 952, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [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(324, 13, F32, 4) (dual of [13, 9, 5]-code or 13-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), 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(1695, 1037, S16, 38) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(3276, 613, F32, 2, 38) (dual of [(613, 2), 1150, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (38, 76, 613)-net over F32 | [i] | ||
| 4 | Linear OOA(3276, 518, F32, 2, 38) (dual of [(518, 2), 960, 39]-NRT-code) | [i] | OOA Folding | |