A further construction of asymptotically optimal codebooks with multiplicative characters

  • Wenjuan Yin
  • Can XiangEmail author
  • Fang-Wei Fu
Original Paper


Codebooks with small inner-product correlation are preferred in many practical applications such as direct spread code division multiple access communications, coding theory, compressed sensing and so on. Heng et al. (IEEE Trans Inf Theory 63(10):6179–6187, 2017), Heng (Discrete Appl Math 250:227–240, 2018) and Luo and Cao (IEEE Trans Inf Theory 64(10):6498–6505, 2018) proposed constructions of asymptotically optimal codebooks via character sums related to Jacobi sums. In this paper, we mainly present a further generalization of the work by Heng (2018). The construction in this paper is an extension and generalization of the above works, and deduces a class of asymptotically optimal codebooks. Furthermore, the parameters of the codebooks are flexible and new.


Codebooks Asymptotic optimality Welch bound Levenstein bound Generalized Jacobi sums 



The authors are very grateful to the two reviewers and the Editor, for their comments and suggestions that improved the presentation and quality of this paper.The research of C. Xiang was supported by the National Natural Science Foundation of China (No. 11701187) and the Ph.D. Start-up Fund of the Natural Science Foundation of Guangdong Province of China (No. 2017A030310522). The research of W. Yin and F. W. Fu was supported by the 973 Program of China (Grant No. 2013CB834204), the National Natural Science Foundation of China (Grant No. 61571243), and the Fundamental Research Funds for the Central Universities of China.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Chern Institute of Mathematics and LPMCNankai UniversityTianjinChina
  2. 2.College of Mathematics and InformaticsSouth China Agricultural UniversityGuangzhouChina

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