2024/03/24 by Sophie Huczynska, Huczynska, Sophie, Sophie Hume +1
Mathematics · #05B10 (Primary) 94A60 #94B60 (Secondary) #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.2403.16284
openalex publication_date 2024/03/24 · openalex created_date 2024/03/27 · openalex updated_date 2026/07/28
Classical strong external difference families (SEDFs) are much-studied combinatorial structures motivated by information security applications; it is conjectured that only one classical abelian SEDF exists with more than two sets. Recently, non-disjoint SEDFs were introduced; it was shown that families of these exist with arbitrarily many sets. We present constructions for both classical and non-disjoint SEDFs, which encompass all known non-cyclotomic examples for either type (plus many new examples) using a sequence-based framework. Moreover, we introduce a range of new external difference structures (allowing set-sizes to vary, and sets to be replaced by multisets) in both the classical and non-disjoint case, and show how these may be applied to various communications applications.