Non-disjoint Strong External Difference Families Can Have Any Number of Sets
Archiv der Mathematik(2024)
摘要
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.
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关键词
Strong external difference families,External difference families,Binary sequences,Optical orthogonal codes,Primary 05B10,Secondary 94A55,20D60
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