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Designs, Codes and Cryptography

, Volume 75, Issue 1, pp 43–57 | Cite as

Two families of nearly optimal codebooks

  • Chengju Li
  • Qin Yue
  • Yiwei Huang
Article

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.

Keywords

Signal theory Difference set Character sums 

Mathematics Subject Classification

94A12 05B10 11T24 

Notes

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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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China
  2. 2.School of SciencesChina Pharmaceutical UniversityNanjingPeople’s Republic of China

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