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Research Article | Open Access

A construction of strongly regular Cayley graphs and their applications to codebooks

Yang Yan1, Xingguo Zhang2,3( ), Rize Jin4,5, Limin Zhou6
School of Information Technology and Engineering, Tianjin University of Technology and Education, Tianjin 300222, China
Engineering Research Center of Integration and Application of Digital Learning Technology, Ministry of Education, Beijing 100039, China
School of Humanities, Tiangong University, Tianjin 300387, China
School of Software, Tiangong University, Tianjin 300387, China
Tianjin Key Laboratory of Autonomous Intelligence Technology and Systems, Tianjin 300387, China
Department of Mathematics, Binzhou University, Binzhou 256600, Shandong Province, China
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Abstract

In this paper, we give a kind of strongly regular Cayley graphs and a class of codebooks. Both constructions are based on choosing subsets of finite fields, and the main tools that we employed are Gauss sums. In particular, these obtained codebooks are asymptotically optimal with respect to the Welch bound and they have new parameters.

Keywords

codebooksstrongly regular Cayley graphsfinite fieldsGauss sumsWelch bound
CLC number: 94B05, 11T23, 11T24, 12E20

References

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AIMS Mathematics
Volume 9 Issue 2,
February 2024
Pages 2672-2683
DOI: 10.3934/math.2024132

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Cite this article:
Yan Y, Zhang X, Jin R, et al. A construction of strongly regular Cayley graphs and their applications to codebooks. AIMS Mathematics, 2024, 9(2): 2672-2683. https://doi.org/10.3934/math.2024132

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Received: 15 November 2023
Revised: 12 December 2023
Accepted: 21 December 2023
Published: 15 February 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)