A construction of finite Frobenius rings and its application to partial difference sets

Abstract

If R is a homomorphic image of a finite Frobenius local ring, there is a known construction that produces Latin square type partial difference sets (PDS) in R × R . By a simple construction, we show that every finite ring is a homomorphic image of a finite Frobenius ring and every finite local ring is a homomorphic image of a finite Frobenius local ring. Consequently, Latin square type PDS can be constructed in R × R for any finite local ring R, where the additive group ( R , + ) can be any finite abelian p-group.