Non-disjoint strong external difference families can have any number of sets

Sophie Huczynska*, Siaw-Lynn Ng

*Corresponding author for this work

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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.
Original languageEnglish
Number of pages11
JournalArchiv der Mathematik
Early online date30 Apr 2024
Publication statusE-pub ahead of print - 30 Apr 2024


  • Strong external difference families
  • External difference families
  • Binary sequences
  • Optical orthogonal codes


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