Circular external difference families: construction and non-existence

The article explores the construction and non-existence of circular external difference families (CEDFs) and strong circular external difference families (SCEDFs), crucial structures in combinatorial design theory. It begins by defining key terms and providing a cyclotomic construction for CEDFs, extending previous results to show the existence of specific CEDFs in finite fields. The study then shifts to SCEDFs, demonstrating that all SCEDFs can be constructed from smaller difference families, and presenting novel non-existence results for certain parameters. The research addresses open problems raised in earlier works, making significant contributions to the field of combinatorial design and its applications in cryptography.