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Two families of nearly optimal codebooks

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Abstract

Codebooks are widely applied in code-division multiple-access systems. Recently, several authors constructed codebooks meeting or nearly meeting the Welch bound (i.e. nearly optimal codebooks) using difference set, almost difference set, relative difference set, and so on. In this paper, we will give two families of nearly optimal codebooks. First, we give a class of new almost difference sets and use them to construct nearly optimal codebooks. Second, we present a general construction of codebooks from partial difference sets and obtain several classes of nearly optimal codebooks.

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Acknowledgments

The paper is supported by NNSF of China (No. 11171150) and Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-13-001). The authors are very grateful to the reviewers and the editor for their valuable comments and suggestions that improved the presentation and quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 211100, People’s Republic of China

    Chengju Li & Qin Yue

  2. School of Sciences, China Pharmaceutical University, Nanjing, People’s Republic of China

    Yiwei Huang

Authors
  1. Chengju Li
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  2. Qin Yue
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  3. Yiwei Huang
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Correspondence to Chengju Li.

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Communicated by J. D. Key.

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Li, C., Yue, Q. & Huang, Y. Two families of nearly optimal codebooks. Des. Codes Cryptogr. 75, 43–57 (2015). https://doi.org/10.1007/s10623-013-9891-7

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  • DOI: https://doi.org/10.1007/s10623-013-9891-7

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