Equivalence Relation on the Set of Subsets of Z_v and Enumeration of the Equivalence Classes

Motivated by the concept of equivalent cyclic difference sets on Z_v (the residue ring modulo v), we introduce a similar equivalence relation on the set of subsets of Z_v as follows. Difinition Let D_1 and D_2 be two subsets of Z_v. If D_1=tD_2+s for some t, s∈Z_v(ged(t,v)=1), then D_1 and D_2 are said to be equivalent, denoted by D_～D_2.