Information on Result #696884
Linear OA(3211, 32776, F32, 4) (dual of [32776, 32765, 5]-code), using construction X4 applied to Ce(3) ⊂ Ce(1) based on
- linear OA(3210, 32768, F32, 4) (dual of [32768, 32758, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(324, 32768, F32, 2) (dual of [32768, 32764, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(327, 8, F32, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,32)), using
- dual of repetition code with length 8 [i]
- linear OA(321, 8, F32, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), 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(3211, 32776, F32, 2, 4) (dual of [(32776, 2), 65541, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (7, 11, 32776)-net over F32 | [i] | ||
| 3 | Linear OOA(3211, 16388, F32, 2, 4) (dual of [(16388, 2), 32765, 5]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3211, 16388, F32, 4, 4) (dual of [(16388, 4), 65541, 5]-NRT-code) | [i] | OA Folding and Stacking | |