Algorithms for difference families in finite abelian groups

TL;DR

This paper extends computational methods for finding difference families from cyclic groups to all finite abelian groups, enhancing search techniques with PSD-test and compression methods.

Contribution

It generalizes existing algorithms for difference families, enabling their application to arbitrary finite abelian groups.

Findings

Successful extension of search algorithms to all finite abelian groups

Effective use of PSD-test and compression methods in the generalized setting

Potential for broader applications in combinatorial design theory

Abstract

Our main objective is to show that the computational methods that we previously developed to search for difference families in cyclic groups can be fully extended to the more general case of arbitrary finite abelian groups. In particular the power density PSD-test and the method of compression can be used to help the search.