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

A cyclic @d-support (n,k)"@m difference family (briefly @d-supp (n,k)"@m-CDF) is a family F of k-subsets of Z"n such that (i) every nonzero element x of Z"n appears in the list @DB of differences of exactly one member B of F; (ii) the number of times that x appears in @DB is at most @m; and (iii) the number of distinct elements appearing in @DB is exactly @d 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 (@d,@m)=(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.

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