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Designs, Codes and Cryptography

, Volume 81, Issue 1, pp 153–168 | Cite as

Complete weight enumerators of some linear codes and their applications

  • Chengju Li
  • Sunghan Bae
  • Jaehyun Ahn
  • Shudi Yang
  • Zheng-An Yao
Article

Abstract

Recently, linear codes constructed from defining sets have been extensively studied. It was shown that the linear codes may have a few nonzero weights or be optimal if the defining sets are well chosen. The weight enumerators of these linear codes were also presented. In this paper, we investigate the complete weight enumerators of some linear codes constructed from the defining sets. As applications, we employ the explicit complete weight enumerators of the linear codes to construct constant composition codes and systematic authentication codes. A new class of optimal constant composition codes and three classes of asymptotically optimal systematic authentication codes are presented.

Keywords

Complete weight enumerators Linear codes Exponential sums Constant composition codes Authentication codes 

Mathematics Subject Classification

94B05 11T71 11T23 94B60 94A62 

Notes

Acknowledgments

The authors are very grateful to the editor and the anonymous reviewers for their valuable comments and suggestions that improved the quality of this paper. This paper is supported by the National Research Foundation of Korea (NRF) Grant funded by the Korea Government (MSIP) (ASARC, NRF-2007-0056093), the National Natural Science Foundation of China (Nos. 11171150, 11271381, 11431015, and 61472457), the Fundamental Research Funds for the Central Universities (No. 56XZA15002), the 973 Program of China (Grant No. 2011CB808000), and the Natural Science Foundation of Guangdong (Grant No. 2014A030313161).

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Chengju Li
    • 1
  • Sunghan Bae
    • 1
  • Jaehyun Ahn
    • 2
  • Shudi Yang
    • 3
    • 4
  • Zheng-An Yao
    • 3
  1. 1.Department of MathematicsKAISTDaejeonKorea
  2. 2.Department of MathematicsChungnam National UniversityDaejeonKorea
  3. 3.Department of MathematicsSun Yat-sen UniversityGuangzhouPeople’s Republic of China
  4. 4.School of Mathematical SciencesQufu Normal UniversityShandongPeople’s Republic of China

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