Information on Result #700481
Linear OA(25663, 65574, F256, 26) (dual of [65574, 65511, 27]-code), using construction X applied to Ce(25) ⊂ Ce(12) based on
- linear OA(25651, 65536, F256, 26) (dual of [65536, 65485, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(25612, 38, F256, 12) (dual of [38, 26, 13]-code or 38-arc in PG(11,256)), using
- discarding factors / shortening the dual code based on linear OA(25612, 256, F256, 12) (dual of [256, 244, 13]-code or 256-arc in PG(11,256)), using
- Reed–Solomon code RS(244,256) [i]
- discarding factors / shortening the dual code based on linear OA(25612, 256, F256, 12) (dual of [256, 244, 13]-code or 256-arc in PG(11,256)), 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, 65574, S128, 26) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25663, 63978, F256, 2, 26) (dual of [(63978, 2), 127893, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25663, 63978, F256, 3, 26) (dual of [(63978, 3), 191871, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(25663, 63978, F256, 4, 26) (dual of [(63978, 4), 255849, 27]-NRT-code) | [i] | ||
| 5 | Linear OOA(25663, 63978, F256, 5, 26) (dual of [(63978, 5), 319827, 27]-NRT-code) | [i] | ||
| 6 | Linear OOA(25663, 63978, F256, 6, 26) (dual of [(63978, 6), 383805, 27]-NRT-code) | [i] | ||
| 7 | Digital (37, 63, 63978)-net over F256 | [i] | ||
| 8 | Linear OOA(25663, 32787, F256, 2, 26) (dual of [(32787, 2), 65511, 27]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25663, 21858, F256, 3, 26) (dual of [(21858, 3), 65511, 27]-NRT-code) | [i] | ||
| 10 | Linear OOA(25663, 16393, F256, 4, 26) (dual of [(16393, 4), 65509, 27]-NRT-code) | [i] | ||
| 11 | Linear OOA(25663, 10929, F256, 6, 26) (dual of [(10929, 6), 65511, 27]-NRT-code) | [i] | ||
| 12 | Linear OOA(25663, 5044, F256, 26, 26) (dual of [(5044, 26), 131081, 27]-NRT-code) | [i] | OA Folding and Stacking | |