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arXiv · 2305.18101

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

Sophie Huczynska·Siaw-Lynn Ng
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Abstract

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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Sophie Huczynska, Siaw-Lynn Ng. 2023-05-29. Non-disjoint strong external difference families can have any number of sets. https://arxiv.org/abs/2305.18101

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