Information on Result #691583
Linear OA(1636, 1048581, F16, 8) (dual of [1048581, 1048545, 9]-code), using construction X applied to Ce(7) ⊂ Ce(6) based on
- linear OA(1636, 1048576, F16, 8) (dual of [1048576, 1048540, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1631, 1048576, F16, 7) (dual of [1048576, 1048545, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-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 | OA(848, 1048581, S8, 8) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(1641, 1048605, F16, 8) (dual of [1048605, 1048564, 9]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1642, 1048821, F16, 8) (dual of [1048821, 1048779, 9]-code) | [i] | ||
| 4 | Linear OOA(1636, 1048581, F16, 2, 8) (dual of [(1048581, 2), 2097126, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (28, 36, 1048581)-net over F16 | [i] | ||
| 6 | Linear OOA(1636, 524290, F16, 2, 8) (dual of [(524290, 2), 1048544, 9]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(1636, 262145, F16, 8, 8) (dual of [(262145, 8), 2097124, 9]-NRT-code) | [i] | OA Folding and Stacking | |