Information on Result #700467
Linear OA(25648, 65565, F256, 20) (dual of [65565, 65517, 21]-code), using construction X applied to Ce(19) ⊂ Ce(9) based on
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(2569, 29, F256, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,256)), using
- discarding factors / shortening the dual code based on linear OA(2569, 256, F256, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), using
- Reed–Solomon code RS(247,256) [i]
- discarding factors / shortening the dual code based on linear OA(2569, 256, F256, 9) (dual of [256, 247, 10]-code or 256-arc in PG(8,256)), 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(12855, 65565, S128, 20) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25648, 57506, F256, 2, 20) (dual of [(57506, 2), 114964, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25648, 57506, F256, 3, 20) (dual of [(57506, 3), 172470, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(25648, 57506, F256, 4, 20) (dual of [(57506, 4), 229976, 21]-NRT-code) | [i] | ||
| 5 | Linear OOA(25648, 57506, F256, 5, 20) (dual of [(57506, 5), 287482, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(25648, 57506, F256, 6, 20) (dual of [(57506, 6), 344988, 21]-NRT-code) | [i] | ||
| 7 | Digital (28, 48, 57506)-net over F256 | [i] | ||
| 8 | Linear OOA(25648, 32782, F256, 2, 20) (dual of [(32782, 2), 65516, 21]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25648, 21855, F256, 3, 20) (dual of [(21855, 3), 65517, 21]-NRT-code) | [i] | ||
| 10 | Linear OOA(25648, 16391, F256, 4, 20) (dual of [(16391, 4), 65516, 21]-NRT-code) | [i] | ||
| 11 | Linear OOA(25648, 13113, F256, 5, 20) (dual of [(13113, 5), 65517, 21]-NRT-code) | [i] | ||