Equivalence Classes of Subsets of a Finite Field

Abstract

For a finite field $F=F(q)$, where $q=p^n$ is a prime power, we will introduce the notion of equivalence of subsets of $F$ which stems out of the equivalence of cyclic difference sets, and give the formulae for the number of equivalence classes of $k$-subsets of $F$ as well as for the number of equivalence classes of subsets of $F$ by using Pólya’s theorem of counting.