Generalizing the case of $\lambda=1$ given by Buratti and Zuanni [Bull Belg. Math. Soc. (1998)], we characterize the $1$-rotational difference families generating a 1-rotational $(v,k,\lambda)$-RBIBD, that is a $(v,k,\lambda)$ resolvable balanced incomplete block design admitting an automorphism group $G$ acting sharply transitively on all but one point $\infty$ and leaving invariant a resolution $\cal R$ of it. When $G$ is transitive on $\cal R$ we prove that removing $\infty$ from a parallel class of $\cal R$ one gets a partitioned difference family, a concept recently introduced by Ding and Yin [IEEE Trans. Inform. Theory, 2005] and used to construct optimal constant composition codes. In this way, by exploiting old and new results about the existence of 1-rotational RBIBDs we are able to derive a great bulk of previously unnoticed partitioned difference families. Among our RBIBDs we construct, in particular, a $(45,5,2)$-RBIBD whose existence was previously in doubt.

A generalized balanced tournament design, or a GBTD(k, m) in short, is a (km, k, k − 1)-BIBD defined on a km-set V . Its blocks can be arranged into an m × (km − 1) array in such a way that (1) every element of V is contained in exactly one cell of each column, and (2) every element of V is contained in at most k cells of each row. In this paper, we present a new construction for GBTDs and show that a GBTD(4, m) exists for any integer m ≥ 5 with at most eight possible exceptions. A link between a GBTD(k, m) and a near constant composition code is also mentioned. The derived code is optimal in the sense of its size.

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As a common generalization of constant weight binary codes and permutation codes, constant composition codes (CCCs) have attracted recent interest due to their numerous applications. In this paper, a class of new CCCs are constructed using design-theoretic techniques. The obtained codes are optimal in the sense of their sizes. This result is established, for the most part, by means of a result on generalized doubly resolvable packings which is of combinatorial interest in its own right.