Information on Result #691621
Linear OA(1693, 1048593, F16, 20) (dual of [1048593, 1048500, 21]-code), using construction X applied to Ce(19) ⊂ Ce(16) based on
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
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(1694, 1048594, F16, 20) (dual of [1048594, 1048500, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1695, 1048595, F16, 20) (dual of [1048595, 1048500, 21]-code) | [i] | ||
| 3 | Linear OOA(1693, 718496, F16, 2, 20) (dual of [(718496, 2), 1436899, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (73, 93, 718496)-net over F16 | [i] | ||
| 5 | Linear OA(1695, 1048596, F16, 20) (dual of [1048596, 1048501, 21]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(1693, 524296, F16, 2, 20) (dual of [(524296, 2), 1048499, 21]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(1693, 104859, F16, 20, 20) (dual of [(104859, 20), 2097087, 21]-NRT-code) | [i] | OA Folding and Stacking | |