A classification of the structures of some Sperner families and superimposed codes

In this paper we will give a new proof by using group action to prove the uniqueness of maximal Sperner families Fmaxn of [n][n]. We will also prove the uniqueness of Sperner families FF of [n][n] with |F|=n⌊n2⌋-1 by using a combinatorial approach. Furthermore, by using the uniqueness of Sperner family, we will classify all the structures of (1,2)(1,2) superimposed codes of size 9×109×10 and 9×119×11.