Geodesic
The number of antichains in ranked partially ordered sets
Diskretnaya Matematika, Tome 1 (1989) no. 1, pp. 35-58.

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We obtain the asymptotic behavior of the number of antichains in partially ordered sets whose diagrams are bipartite graphs that possess extension properties and whose number of vertices does not exceed $c\log_2\kappa$, where $\kappa$ is the minimum of the degrees of the vertices and $c$ is a constant less than 3. As a consequence we obtain the well-known asymptotic behavior of the number of binary codes with distance 2. 
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A. A. Sapozhenko. The number of antichains in ranked partially ordered sets. Diskretnaya Matematika, Tome 1 (1989) no. 1, pp. 35-58. http://geodesic.mathdoc.fr/item/DM_1989_1_1_a7/