Information on Result #700475
Linear OA(25653, 65568, F256, 22) (dual of [65568, 65515, 23]-code), using construction X applied to Ce(21) ⊂ Ce(10) 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(25621, 65536, F256, 11) (dual of [65536, 65515, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(12861, 65568, S128, 22) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25653, 59446, F256, 2, 22) (dual of [(59446, 2), 118839, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25653, 59446, F256, 3, 22) (dual of [(59446, 3), 178285, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(25653, 59446, F256, 4, 22) (dual of [(59446, 4), 237731, 23]-NRT-code) | [i] | ||
| 5 | Linear OOA(25653, 59446, F256, 5, 22) (dual of [(59446, 5), 297177, 23]-NRT-code) | [i] | ||
| 6 | Linear OOA(25653, 59446, F256, 6, 22) (dual of [(59446, 6), 356623, 23]-NRT-code) | [i] | ||
| 7 | Digital (31, 53, 59446)-net over F256 | [i] | ||
| 8 | Linear OOA(25653, 32784, F256, 2, 22) (dual of [(32784, 2), 65515, 23]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25653, 21856, F256, 3, 22) (dual of [(21856, 3), 65515, 23]-NRT-code) | [i] | ||
| 10 | Linear OOA(25653, 16392, F256, 4, 22) (dual of [(16392, 4), 65515, 23]-NRT-code) | [i] | ||
| 11 | Linear OOA(25653, 10928, F256, 6, 22) (dual of [(10928, 6), 65515, 23]-NRT-code) | [i] | ||