Information on Result #700459
Linear OA(25647, 65562, F256, 20) (dual of [65562, 65515, 21]-code), using construction X applied to Ce(19) ⊂ Ce(10) 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(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(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(12854, 65562, S128, 20) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25647, 42257, F256, 2, 20) (dual of [(42257, 2), 84467, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25647, 42257, F256, 3, 20) (dual of [(42257, 3), 126724, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(25647, 42257, F256, 4, 20) (dual of [(42257, 4), 168981, 21]-NRT-code) | [i] | ||
| 5 | Linear OOA(25647, 42257, F256, 5, 20) (dual of [(42257, 5), 211238, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(25647, 42257, F256, 6, 20) (dual of [(42257, 6), 253495, 21]-NRT-code) | [i] | ||
| 7 | Digital (27, 47, 42257)-net over F256 | [i] | ||
| 8 | Linear OOA(25647, 32781, F256, 2, 20) (dual of [(32781, 2), 65515, 21]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25647, 21854, F256, 3, 20) (dual of [(21854, 3), 65515, 21]-NRT-code) | [i] | ||
| 10 | Linear OOA(25647, 16390, F256, 4, 20) (dual of [(16390, 4), 65513, 21]-NRT-code) | [i] | ||
| 11 | Linear OOA(25647, 13112, F256, 5, 20) (dual of [(13112, 5), 65513, 21]-NRT-code) | [i] | ||
| 12 | Linear OOA(25647, 10927, F256, 6, 20) (dual of [(10927, 6), 65515, 21]-NRT-code) | [i] | ||
| 13 | Linear OOA(25647, 6556, F256, 20, 20) (dual of [(6556, 20), 131073, 21]-NRT-code) | [i] | OA Folding and Stacking | |