Some New Constructions of Difference Systems of Sets

Abstract

Difference systems of sets (DSSs) are combinatorial structures introduced by Levenshtein, which are a generalization of cyclic difference sets and arise in connection with code synchronization. In this paper, we describe four direct constructions of optimal DSSs from finite projective geometries and present a recursive construction of DSSs by extending the known construction. As a consequence, new infinite families of optimal DSSs can be obtained.