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Some New Constructions of Difference Systems of Sets

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Abstract

Difference systems of sets (DSSs) are combinatorial structures introduced by Levenshtein, which are a generalization of cyclic difference sets and arise in connection with code synchronization. In this paper, we describe four direct constructions of optimal DSSs from finite projective geometries and present a recursive construction of DSSs by extending the known construction. As a consequence, new infinite families of optimal DSSs can be obtained.

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Acknowledgements

We would like to thank the anonymous reviewers for many valuable suggestions that allowed us to improve the paper.

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  1. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, China

    Shuyu Shen & Jingjun Bao

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  1. Shuyu Shen
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  2. Jingjun Bao
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Correspondence to Jingjun Bao.

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Shen, S., Bao, J. Some New Constructions of Difference Systems of Sets. Graphs and Combinatorics 40, 6 (2024). https://doi.org/10.1007/s00373-023-02729-6

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