Information on Result #700278
Linear OA(25640, 65560, F256, 17) (dual of [65560, 65520, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,4]) based on
- linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(2567, 23, F256, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,256)), using
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), using
- Reed–Solomon code RS(249,256) [i]
- discarding factors / shortening the dual code based on linear OA(2567, 256, F256, 7) (dual of [256, 249, 8]-code or 256-arc in PG(6,256)), 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(12846, 65560, S128, 17) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25640, 45982, F256, 2, 17) (dual of [(45982, 2), 91924, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25640, 45982, F256, 3, 17) (dual of [(45982, 3), 137906, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(25640, 45982, F256, 4, 17) (dual of [(45982, 4), 183888, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(25640, 45982, F256, 5, 17) (dual of [(45982, 5), 229870, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(25640, 45982, F256, 6, 17) (dual of [(45982, 6), 275852, 18]-NRT-code) | [i] | ||
| 7 | Digital (23, 40, 45982)-net over F256 | [i] | ||
| 8 | Linear OOA(25640, 32780, F256, 2, 17) (dual of [(32780, 2), 65520, 18]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25640, 21853, F256, 3, 17) (dual of [(21853, 3), 65519, 18]-NRT-code) | [i] | ||
| 10 | Linear OOA(25640, 16390, F256, 4, 17) (dual of [(16390, 4), 65520, 18]-NRT-code) | [i] | ||
| 11 | Linear OOA(25640, 13112, F256, 5, 17) (dual of [(13112, 5), 65520, 18]-NRT-code) | [i] | ||