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Research Article | Open Access

A class of nearly optimal codebooks and their applications in strongly regular Cayley graphs

Qiuyan Wang1,2, Weixin Liu1( ), Jianming Wang1,2, Yang Yan3
School of Computer Science and Technology, Tiangong University, Tianjin 300387 China
Tianjin Key Laboratory of Autonomous Intelligence Technology and Systems, Tiangong University, Tianjin 300387, China
School of Information Technology and Engineering, Tianjin University of Technology and Education, Tianjin 300222 China
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Abstract

Codebooks with small inner-product correlations are desirable in many fields, including compressed sensing, direct spread code division multiple access (CDMA) systems, and space-time codes. The objective of this paper is to present a class of codebooks and explore their applications in strongly regular Cayley graphs. The obtained codebooks are nearly optimal in the sense that their maximum cross-correlation amplitude nearly meets the Welch bound. As far as we know, this construction of codebooks provides new parameters.

Keywords

codebookcharacterfinite fieldsignal setWelch bound
CLC number: 94B05, 11T23, 11T24, 12E20

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AIMS Mathematics
Volume 9 Issue 7,
July 2024
Pages 18236-18246
DOI: 10.3934/math.2024890

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Cite this article:
Wang Q, Liu W, Wang J, et al. A class of nearly optimal codebooks and their applications in strongly regular Cayley graphs. AIMS Mathematics, 2024, 9(7): 18236-18246. https://doi.org/10.3934/math.2024890

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Received: 01 February 2024
Revised: 15 May 2024
Accepted: 27 May 2024
Published: 15 July 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)