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AIMS Mathematics

2024, Volume 9, Issue 4: 9631-9640. doi: 10.3934/math.2024471
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Research article

A new construction of asymptotically optimal 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.
    Tianjin Swom Technology Development Co., Ltd., Tianjin 300387, China
  • 4.
    School of Computer Science, Tiangong University, Tianjin 300387, China
  • 5.
    Tianjin Key Laboratory of Autonomous Intelligence Technology and Systems, Tianjin 300387, China
  • 6.
    College of Science, Civil Aviation University of China, Tianjin 300300, China
  • Received: 15 January 2024 Revised: 23 February 2024 Accepted: 01 March 2024 Published: 11 March 2024

  • MSC : 11T23, 11T24, 12E20, 94B05

  • 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.

    Citation: Yang Yan, Hanning Chen, Jianming Wang, Gang Wang. A new construction of asymptotically optimal codebooks[J]. AIMS Mathematics, 2024, 9(4): 9631-9640. doi: 10.3934/math.2024471

    Related Papers:

  • 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.


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  • © 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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