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Complete weight enumerators of a class of two-weight linear codes

  • Shudi Yang
  • Qin Yue
  • Yansheng Wu
  • Xiangli Kong
Article
  • 71 Downloads

Abstract

Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. For an odd prime \(p\), we determine the complete weight enumerator and weight enumerator of a class of \(p\)-ary linear codes by choosing a proper defining set. The results show that they have at most two weights and are suitable for applications in secret sharing schemes.

Keywords

Linear code Complete weight enumerator Weight enumerator Exponential sum 

Mathematics Subject Classification (2010)

94B15 11T71 

Notes

Acknowledgements

The work is partially supported by the National Natural Science Foundation of China (11701317, 61772015, 61472457, 11571380), China Postdoctoral Science Foundation Funded Project (2017M611801) and Jiangsu Planned Projects for Postdoctoral Research Funds (1701104C). This work is also partially supported by Guangzhou Science and Technology Program (201607010144) and the Natural Science Foundation of Shandong Province of China (ZR2016AM04).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Shudi Yang
    • 1
  • Qin Yue
    • 2
  • Yansheng Wu
    • 2
  • Xiangli Kong
    • 1
  1. 1.School of Mathematical SciencesQufu Normal UniversityShandongPeople’s Republic of China
  2. 2.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China

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