From a 1-Rotational RBIBD to a Partitioned Difference Family

Generalizing the case of λ = 1 given by Buratti and Zuanni [Bull Belg. Math. Soc. (1998)], we characterize the 1-rotational difference families generating a 1rotational (v, k, λ)-RBIBD, that is a (v, k, λ) resolvable balanced incomplete block design admitting an automorphism group G acting sharply transitively on all but one point ∞ and leaving invariant a resolution R of it. When G is transitive on R we prove that removing ∞ from a parallel class of 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.