2023/05/29 by Huczynska, Sophie, Ng, Siaw-Lynn
#05B10 #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2305.18101
Strong external difference families (SEDFs) are much-studied combinatorial objects motivated by an information security application. A well-known conjecture states that only one abelian SEDF with more than 2 sets exists. We show that if the disjointness condition is replaced by non-disjointness, then abelian SEDFs can be constructed with more than 2 sets (indeed any number of sets). We demonstrate that the non-disjoint analogue has striking differences to, and connections with, the classical SEDF and arises naturally via another coding application.