Information on Result #880081
Linear OOA(25634, 32777, F256, 2, 15) (dual of [(32777, 2), 65520, 16]-NRT-code), using OOA 2-folding based on linear OA(25634, 65554, F256, 15) (dual of [65554, 65520, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,4]) [i] based on
- linear OA(25629, 65537, F256, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(2565, 17, F256, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,256)), using
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), using
- Reed–Solomon code RS(251,256) [i]
- discarding factors / shortening the dual code based on linear OA(2565, 256, F256, 5) (dual of [256, 251, 6]-code or 256-arc in PG(4,256)), 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(25634, 32777, F256, 3, 15) (dual of [(32777, 3), 98297, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(25634, 32777, F256, 4, 15) (dual of [(32777, 4), 131074, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(25634, 32777, F256, 5, 15) (dual of [(32777, 5), 163851, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(25634, 32777, F256, 6, 15) (dual of [(32777, 6), 196628, 16]-NRT-code) | [i] | ||
| 5 | Digital (19, 34, 32777)-net over F256 | [i] | ||