Non-disjoint strong external difference families can have any number of sets
Combinatorics
2023-05-30 v1
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.
Keywords
Cite
@article{arxiv.2305.18101,
title = {Non-disjoint strong external difference families can have any number of sets},
author = {Sophie Huczynska and Siaw-Lynn Ng},
journal= {arXiv preprint arXiv:2305.18101},
year = {2023}
}