Two Classes of Partitioned Uniform Cyclic Relative Difference Families and Their Applications to Difference Systems of Sets

The concept of “relative difference family”, denoted by [Formula: see text]-RDF, was introduced by M. Buratti in 1998. Especially cyclic RDFs with [Formula: see text] are closely related to the concept of “optical orthogonal codes”. However, to the best of our knowledge, few studies on partitioned RDFs with [Formula: see text] have been reported in the literature to date. In this paper, we establish two results to characterize partitioned RDFs, among which a lower bound is used to achieve optimality in applications and determine the size of base blocks of partitioned RDFs. As the main contribution, two classes of partitioned uniform cyclic RDFs with [Formula: see text] are proposed by means of some specific mappings. Employing these partitioned uniform cyclic RDFs, we obtain regular and optimal difference systems of sets with flexible parameters at the same time.