Strong External Difference Families and Classification of α‐Valuations

ABSTRACT One method of constructing ‐SEDFs (i.e., strong external difference families) in makes use of ‐valuations of complete bipartite graphs . We explore this approach and we provide a classification theorem which shows that all such ‐valuations can be constructed recursively via a sequence of “blow‐up” operations. We also enumerate all ‐SEDFs in for and we show that all these SEDFs are equivalent to ‐valuations via affine transformations. Whether this holds for all as well is an interesting open problem. We also study SEDFs in dihedral groups, where we show that two known constructions are equivalent.