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.