Information on Result #731610
Linear OA(1684, 131084, F16, 21) (dual of [131084, 131000, 22]-code), using trace code based on linear OA(25642, 65542, F256, 21) (dual of [65542, 65500, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,9]) [i] 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(1685, 131085, F16, 21) (dual of [131085, 131000, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1684, 96202, F16, 2, 21) (dual of [(96202, 2), 192320, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (63, 84, 96202)-net over F16 | [i] | ||
| 4 | Linear OOA(1684, 65542, F16, 2, 21) (dual of [(65542, 2), 131000, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1684, 13108, F16, 21, 21) (dual of [(13108, 21), 275184, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |