Information on Result #691620
Linear OA(1698, 1048593, F16, 21) (dual of [1048593, 1048495, 22]-code), using construction X applied to Ce(20) ⊂ Ce(17) based on
- linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(1699, 1048594, F16, 21) (dual of [1048594, 1048495, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1698, 742109, F16, 2, 21) (dual of [(742109, 2), 1484120, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (77, 98, 742109)-net over F16 | [i] | ||
| 4 | Linear OOA(1698, 524296, F16, 2, 21) (dual of [(524296, 2), 1048494, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1698, 104859, F16, 21, 21) (dual of [(104859, 21), 2201941, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |