Abstract: | The concept of a (q, k, λ, t) almost difference family (ADF) has been introduced and studied by C. Ding and J. Yin as a useful generalization of the concept of an almost difference set. In this paper, we consider, more generally, (q, K, λ, t, Q)-ADFs, where K = {k1, k2, ..., kr} is a set of positive integers and Q = (q1, q2,..., qr) is a given block-size distribution sequence. A necessary condition for the existence of a (q, K, λ, t, Q)-ADF is given, and several infinite classes of (q, K, λ, t, Q)-ADFs are constructed. |