Information on Result #700240
Linear OA(25642, 65542, F256, 21) (dual of [65542, 65500, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,9]) 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(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(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(1684, 131084, F16, 21) (dual of [131084, 131000, 22]-code) | [i] | Trace Code | |
| 2 | OA(3268, 65542, S32, 21) | [i] | Discarding Parts of the Base for OAs | |
| 3 | OA(6456, 65542, S64, 21) | [i] | ||
| 4 | OA(12848, 65542, S128, 21) | [i] | ||
| 5 | Linear OA(25652, 65799, F256, 21) (dual of [65799, 65747, 22]-code) | [i] | (u, u+v)-Construction | |
| 6 | Linear OA(25653, 65802, F256, 21) (dual of [65802, 65749, 22]-code) | [i] | ||
| 7 | Linear OA(25654, 65804, F256, 21) (dual of [65804, 65750, 22]-code) | [i] | ||
| 8 | Linear OA(25655, 65806, F256, 21) (dual of [65806, 65751, 22]-code) | [i] | ||
| 9 | Linear OOA(25642, 32771, F256, 2, 21) (dual of [(32771, 2), 65500, 22]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(25642, 21847, F256, 3, 21) (dual of [(21847, 3), 65499, 22]-NRT-code) | [i] | ||
| 11 | Linear OOA(25642, 16385, F256, 4, 21) (dual of [(16385, 4), 65498, 22]-NRT-code) | [i] | ||
| 12 | Linear OOA(25642, 13108, F256, 5, 21) (dual of [(13108, 5), 65498, 22]-NRT-code) | [i] | ||
| 13 | Linear OOA(25642, 6554, F256, 21, 21) (dual of [(6554, 21), 137592, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |