Information on Result #700277
Linear OA(25644, 65560, F256, 19) (dual of [65560, 65516, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,5]) based on
- linear OA(25637, 65537, F256, 19) (dual of [65537, 65500, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (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(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(12851, 65560, S128, 19) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25644, 34733, F256, 2, 19) (dual of [(34733, 2), 69422, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25644, 34733, F256, 3, 19) (dual of [(34733, 3), 104155, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(25644, 34733, F256, 4, 19) (dual of [(34733, 4), 138888, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(25644, 34733, F256, 5, 19) (dual of [(34733, 5), 173621, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(25644, 34733, F256, 6, 19) (dual of [(34733, 6), 208354, 20]-NRT-code) | [i] | ||
| 7 | Digital (25, 44, 34733)-net over F256 | [i] | ||
| 8 | Linear OOA(25644, 32780, F256, 2, 19) (dual of [(32780, 2), 65516, 20]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25644, 21853, F256, 3, 19) (dual of [(21853, 3), 65515, 20]-NRT-code) | [i] | ||
| 10 | Linear OOA(25644, 16390, F256, 4, 19) (dual of [(16390, 4), 65516, 20]-NRT-code) | [i] | ||
| 11 | Linear OOA(25644, 13112, F256, 5, 19) (dual of [(13112, 5), 65516, 20]-NRT-code) | [i] | ||
| 12 | Linear OOA(25644, 7284, F256, 19, 19) (dual of [(7284, 19), 138352, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |