Information on Result #696727
Linear OA(3220, 32777, F32, 7) (dual of [32777, 32757, 8]-code), using construction X4 applied to C([0,3]) ⊂ C([0,2]) based on
- linear OA(3219, 32769, F32, 7) (dual of [32769, 32750, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(3213, 32769, F32, 5) (dual of [32769, 32756, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [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(3220, 32777, F32, 2, 7) (dual of [(32777, 2), 65534, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (13, 20, 32777)-net over F32 | [i] | ||