Information on Result #700283
Linear OA(25650, 65566, F256, 21) (dual of [65566, 65516, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,5]) based on
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [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(12858, 65566, S128, 21) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25650, 50504, F256, 2, 21) (dual of [(50504, 2), 100958, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25650, 50504, F256, 3, 21) (dual of [(50504, 3), 151462, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(25650, 50504, F256, 4, 21) (dual of [(50504, 4), 201966, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(25650, 50504, F256, 5, 21) (dual of [(50504, 5), 252470, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(25650, 50504, F256, 6, 21) (dual of [(50504, 6), 302974, 22]-NRT-code) | [i] | ||
| 7 | Digital (29, 50, 50504)-net over F256 | [i] | ||
| 8 | Linear OOA(25650, 32783, F256, 2, 21) (dual of [(32783, 2), 65516, 22]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25650, 21855, F256, 3, 21) (dual of [(21855, 3), 65515, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(25650, 16391, F256, 4, 21) (dual of [(16391, 4), 65514, 22]-NRT-code) | [i] | ||
| 11 | Linear OOA(25650, 13113, F256, 5, 21) (dual of [(13113, 5), 65515, 22]-NRT-code) | [i] | ||