Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of difference families and the variations in priorities in constructions. We propose a definition of disjoint difference families that encompasses these variations and...

Some block disjoint difference families are constructed in rings with the property that there are k distinct units uit 0 < i < k — 1, such that differences ut — Uj (0 < i < j < k — 1) are all units. These constructions are utilized to produce a large number of classes of resolvable block designs.

Strong difference families are an interesting class of discrete structures which can be used to derive relative difference families. Relative difference families are closely related to 2-designs, and have applications in constructions for many significant codes, such as optical orthogonal codes and optical orthogonal signature pattern codes. In this paper, with a careful use of cyclotomic condi...

In this paper, we give new constructions of disjoint difference families from Galois rings. The constructions are based on choosing cosets of the unit group of a subring in the Galois ring GR(p2, p2s). Two infinite families of disjoint difference families are obtained from the Galois rings GR(p2, p4n) and GR(22, 22s).