Information on Result #691585
Linear OA(1631, 1048581, F16, 7) (dual of [1048581, 1048550, 8]-code), using construction X applied to Ce(6) ⊂ Ce(5) based on
- 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(1626, 1048576, F16, 6) (dual of [1048576, 1048550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(842, 1048581, S8, 7) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(1634, 1048599, F16, 7) (dual of [1048599, 1048565, 8]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(1635, 1048838, F16, 7) (dual of [1048838, 1048803, 8]-code) | [i] | ||
| 4 | Linear OA(1636, 1049210, F16, 7) (dual of [1049210, 1049174, 8]-code) | [i] | ||
| 5 | Linear OOA(1631, 1048581, F16, 2, 7) (dual of [(1048581, 2), 2097131, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (24, 31, 1048581)-net over F16 | [i] | ||
| 7 | Linear OOA(1631, 524290, F16, 2, 7) (dual of [(524290, 2), 1048549, 8]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(1631, 349526, F16, 7, 7) (dual of [(349526, 7), 2446651, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |