Information on Result #700470
Linear OA(25663, 65568, F256, 27) (dual of [65568, 65505, 28]-code), using construction X applied to Ce(26) ⊂ Ce(15) based on
- linear OA(25653, 65536, F256, 27) (dual of [65536, 65483, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(25610, 32, F256, 10) (dual of [32, 22, 11]-code or 32-arc in PG(9,256)), using
- discarding factors / shortening the dual code based on linear OA(25610, 256, F256, 10) (dual of [256, 246, 11]-code or 256-arc in PG(9,256)), using
- Reed–Solomon code RS(246,256) [i]
- discarding factors / shortening the dual code based on linear OA(25610, 256, F256, 10) (dual of [256, 246, 11]-code or 256-arc in PG(9,256)), 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(12872, 65568, S128, 27) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25663, 37444, F256, 2, 27) (dual of [(37444, 2), 74825, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25663, 37444, F256, 3, 27) (dual of [(37444, 3), 112269, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(25663, 37444, F256, 4, 27) (dual of [(37444, 4), 149713, 28]-NRT-code) | [i] | ||
| 5 | Linear OOA(25663, 37444, F256, 5, 27) (dual of [(37444, 5), 187157, 28]-NRT-code) | [i] | ||
| 6 | Linear OOA(25663, 37444, F256, 6, 27) (dual of [(37444, 6), 224601, 28]-NRT-code) | [i] | ||
| 7 | Digital (36, 63, 37444)-net over F256 | [i] | ||
| 8 | Linear OOA(25663, 32784, F256, 2, 27) (dual of [(32784, 2), 65505, 28]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25663, 21856, F256, 3, 27) (dual of [(21856, 3), 65505, 28]-NRT-code) | [i] | ||
| 10 | Linear OOA(25663, 16392, F256, 4, 27) (dual of [(16392, 4), 65505, 28]-NRT-code) | [i] | ||
| 11 | Linear OOA(25663, 10928, F256, 6, 27) (dual of [(10928, 6), 65505, 28]-NRT-code) | [i] | ||