Information on Result #700247
Linear OA(25614, 65542, F256, 7) (dual of [65542, 65528, 8]-code), using construction X applied to C([0,3]) ⊂ C([0,2]) based on
- linear OA(25613, 65537, F256, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(2569, 65537, F256, 5) (dual of [65537, 65528, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 | Linear OA(1628, 131084, F16, 7) (dual of [131084, 131056, 8]-code) | [i] | Trace Code | |
| 2 | OA(12816, 65542, S128, 7) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OA(25618, 131079, F256, 7) (dual of [131079, 131061, 8]-code) | [i] | (u, u+v)-Construction | |
| 4 | Linear OOA(25614, 32771, F256, 2, 7) (dual of [(32771, 2), 65528, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(25614, 21847, F256, 3, 7) (dual of [(21847, 3), 65527, 8]-NRT-code) | [i] | ||
| 6 | Linear OOA(25614, 21847, F256, 4, 7) (dual of [(21847, 4), 87374, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 7 | Linear OOA(25614, 21847, F256, 5, 7) (dual of [(21847, 5), 109221, 8]-NRT-code) | [i] | ||
| 8 | Linear OOA(25614, 21847, F256, 6, 7) (dual of [(21847, 6), 131068, 8]-NRT-code) | [i] | ||