On cyclic 2(k−1)-support (n,k)k−1 difference families

A cyclic δ-support (n,k)μ difference family (briefly δ-supp (n,k)μ-CDF) is a family F of k-subsets of Zn such that (i) every nonzero element x of Zn appears in the list ΔB of differences of exactly one member B of F; (ii) the number of times that x appears in ΔB is at most μ; and (iii) the number of distinct elements appearing in ΔB is exactly δ for every B∈F. The study of this concept is motivated by applications for multiple-access communication systems.In this paper, we treat the case when (δ,μ)=(2(k−1),k−1) and discuss about the existence of 2(k−1)-supp (p,k)k−1-CDFs with p primes in relation to the problem of perfect packings. Furthermore, we prove that the set of primes p for which there exist 2(k−1)-supp (p,k)k−1-CDFs is infinite for the cases k=4 and 5 by investigating the Kronecker density.