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Two kinds of constructions of directed strongly regular graphs

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Abstract

In this paper, we construct directed strongly regular graphs with new parameters by using partial sum families with local rings. 16 families of new directed strongly regular graphs are obtained and the uniform partial sum families are given. Based on the cyclotomic numbers of finite fields, we present two infinite families of directed strongly regular Cayley graphs from semi-direct products of groups.

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Acknowledgements

We are grateful to Prof. Tao Feng for many useful discussions. We thank to the reviewers for numerous helpful comments. The work of the first two authors was supported by National Natural Science Foundation of China under Grant No. 11771392.

Funding

National Natural Science Foundation of China under Grant No. 11771392.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China

    Jingkun Zhou & Zhiwen He

  2. School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Zhao Chai

Authors
  1. Jingkun Zhou
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  2. Zhiwen He
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  3. Zhao Chai
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Correspondence to Zhiwen He.

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Communicated by Y. Zhou.

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Zhou, J., He, Z. & Chai, Z. Two kinds of constructions of directed strongly regular graphs. Des. Codes Cryptogr. 89, 255–268 (2021). https://doi.org/10.1007/s10623-020-00817-9

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  • DOI: https://doi.org/10.1007/s10623-020-00817-9

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