Average of complete joint weight enumerators and self-dual codes

In this paper, we give a representation of the average of complete joint weight enumerators of two linear codes of length $n$ over ${\mathbb{F}}_q$ and ${\mathbb{Z}}_k$ in terms of the compositions of $n$ and their distributions in the codes. We also obtain a generalization of the representation for the average of $g$-fold complete joint weight enumerators of codes over ${\mathbb{F}}_q$ and ${\mathbb{Z}}_k$. Finally, the average of intersection numbers of a pair of Type III (resp. Type IV) codes, and its second moment are found.