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AIMS Mathematics

2024, Volume 9, Issue 2: 2672-2683. doi: 10.3934/math.2024132
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Research article

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

  • 1.
    School of Information Technology and Engineering, Tianjin University of Technology and Education, Tianjin 300222, China
  • 2.
    Engineering Research Center of Integration and Application of Digital Learning Technology, Ministry of Education, Beijing 100039, China
  • 3.
    School of Humanities, Tiangong University, Tianjin 300387, China
  • 4.
    School of Software, Tiangong University, Tianjin 300387, China
  • 5.
    Tianjin Key Laboratory of Autonomous Intelligence Technology and Systems, Tianjin 300387, China
  • 6.
    Department of Mathematics, Binzhou University, Binzhou 256600, Shandong Province, China
  • Received: 15 November 2023 Revised: 12 December 2023 Accepted: 21 December 2023 Published: 27 December 2023

  • MSC : 94B05, 11T23, 11T24, 12E20

  • 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.

    Citation: Yang Yan, Xingguo Zhang, Rize Jin, Limin Zhou. A construction of strongly regular Cayley graphs and their applications to codebooks[J]. AIMS Mathematics, 2024, 9(2): 2672-2683. doi: 10.3934/math.2024132

    Related Papers:

  • 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.


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