Information on Result #700457
Linear OA(25651, 65562, F256, 22) (dual of [65562, 65511, 23]-code), using construction X applied to Ce(21) ⊂ Ce(12) based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25625, 65536, F256, 13) (dual of [65536, 65511, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2568, 26, F256, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,256)), using
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), using
- Reed–Solomon code RS(248,256) [i]
- discarding factors / shortening the dual code based on linear OA(2568, 256, F256, 8) (dual of [256, 248, 9]-code or 256-arc in PG(7,256)), 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(12859, 65562, S128, 22) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25651, 34139, F256, 2, 22) (dual of [(34139, 2), 68227, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25651, 34139, F256, 3, 22) (dual of [(34139, 3), 102366, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(25651, 34139, F256, 4, 22) (dual of [(34139, 4), 136505, 23]-NRT-code) | [i] | ||
| 5 | Linear OOA(25651, 34139, F256, 5, 22) (dual of [(34139, 5), 170644, 23]-NRT-code) | [i] | ||
| 6 | Linear OOA(25651, 34139, F256, 6, 22) (dual of [(34139, 6), 204783, 23]-NRT-code) | [i] | ||
| 7 | Digital (29, 51, 34139)-net over F256 | [i] | ||
| 8 | Linear OOA(25651, 32781, F256, 2, 22) (dual of [(32781, 2), 65511, 23]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25651, 21854, F256, 3, 22) (dual of [(21854, 3), 65511, 23]-NRT-code) | [i] | ||
| 10 | Linear OOA(25651, 16390, F256, 4, 22) (dual of [(16390, 4), 65509, 23]-NRT-code) | [i] | ||
| 11 | Linear OOA(25651, 13112, F256, 5, 22) (dual of [(13112, 5), 65509, 23]-NRT-code) | [i] | ||
| 12 | Linear OOA(25651, 10927, F256, 6, 22) (dual of [(10927, 6), 65511, 23]-NRT-code) | [i] | ||
| 13 | Linear OOA(25651, 5960, F256, 22, 22) (dual of [(5960, 22), 131069, 23]-NRT-code) | [i] | OA Folding and Stacking | |