Circular external difference families: construction and non-existence

The circular external difference family and its strong version are of great significance both in theory and in applications. In this paper, we apply the classical cyclotomic construction to the circular external differnece family and exhibit several concrete examples, in particular constructing an infinite family. Furthermore, we prove that all strong circular external differnece families are constructed by patching together several strong external difference families consisting of two subsets, thereby solving the open problem raised by Veitch and Stinson. We also present a new result on the non-existence of a certain type of strong external difference families.