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Research Article | Open Access

A new construction of asymptotically optimal codebooks

Yang Yan1, Hanning Chen2,3,4( ), Jianming Wang4,5, Gang Wang6
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
Tianjin Swom Technology Development Co., Ltd., Tianjin 300387, China
School of Computer Science, Tiangong University, Tianjin 300387, China
Tianjin Key Laboratory of Autonomous Intelligence Technology and Systems, Tianjin 300387, China
College of Science, Civil Aviation University of China, Tianjin 300300, China
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Abstract

Codebooks with small cross-correlation amplitude have extensive applications in many fields including code division multiple access (CDMA) communications systems, space-time codes, and compressed sensing. In this paper, a class of asymptotically optimal codebooks was constructed, and the maximum inner-product of these presented codebooks was determined by using properties of character sums over finite fields. Furthermore, these codebooks provided new parameters.

Keywords

codebookscharactersfinite fieldsasymptotical optimalityWelch bound
CLC number: 11T23, 11T24, 12E20, 94B05

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 9631-9640
DOI: 10.3934/math.2024471

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Cite this article:
Yan Y, Chen H, Wang J, et al. A new construction of asymptotically optimal codebooks. AIMS Mathematics, 2024, 9(4): 9631-9640. https://doi.org/10.3934/math.2024471

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Received: 15 January 2024
Revised: 23 February 2024
Accepted: 01 March 2024
Published: 15 April 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)