Strong External Difference Families and Classification of α-Valuations

Document Type

Article

Publication Date

1-1-2025

Abstract

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

Publication Title

Journal of Combinatorial Designs

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