Information on Result #691615
Linear OA(16123, 1048593, F16, 26) (dual of [1048593, 1048470, 27]-code), using construction X applied to Ce(25) ⊂ Ce(22) based on
- linear OA(16121, 1048576, F16, 26) (dual of [1048576, 1048455, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(16124, 1048594, F16, 26) (dual of [1048594, 1048470, 27]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16123, 863393, F16, 2, 26) (dual of [(863393, 2), 1726663, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (97, 123, 863393)-net over F16 | [i] | ||
| 4 | Linear OOA(16123, 524296, F16, 2, 26) (dual of [(524296, 2), 1048469, 27]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(16123, 80661, F16, 26, 26) (dual of [(80661, 26), 2097063, 27]-NRT-code) | [i] | OA Folding and Stacking | |