Information on Result #700285
Linear OA(25664, 65572, F256, 27) (dual of [65572, 65508, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,7]) based on
- linear OA(25653, 65537, F256, 27) (dual of [65537, 65484, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- 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(25611, 35, F256, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,256)), using
- discarding factors / shortening the dual code based on linear OA(25611, 256, F256, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), using
- Reed–Solomon code RS(245,256) [i]
- discarding factors / shortening the dual code based on linear OA(25611, 256, F256, 11) (dual of [256, 245, 12]-code or 256-arc in PG(10,256)), 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 | OA(12874, 65572, S128, 27) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25664, 46746, F256, 2, 27) (dual of [(46746, 2), 93428, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25664, 46746, F256, 3, 27) (dual of [(46746, 3), 140174, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(25664, 46746, F256, 4, 27) (dual of [(46746, 4), 186920, 28]-NRT-code) | [i] | ||
| 5 | Linear OOA(25664, 46746, F256, 5, 27) (dual of [(46746, 5), 233666, 28]-NRT-code) | [i] | ||
| 6 | Linear OOA(25664, 46746, F256, 6, 27) (dual of [(46746, 6), 280412, 28]-NRT-code) | [i] | ||
| 7 | Digital (37, 64, 46746)-net over F256 | [i] | ||
| 8 | Linear OOA(25664, 32786, F256, 2, 27) (dual of [(32786, 2), 65508, 28]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25664, 21857, F256, 3, 27) (dual of [(21857, 3), 65507, 28]-NRT-code) | [i] | ||
| 10 | Linear OOA(25664, 16393, F256, 4, 27) (dual of [(16393, 4), 65508, 28]-NRT-code) | [i] | ||
| 11 | Linear OOA(25664, 13114, F256, 5, 27) (dual of [(13114, 5), 65506, 28]-NRT-code) | [i] | ||