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Designs, Codes and Cryptography

, Volume 82, Issue 3, pp 663–674 | Cite as

Complete weight enumerators of a family of three-weight linear codes

  • Shudi Yang
  • Zheng-An Yao
Article

Abstract

Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime p, we present the explicit complete weight enumerator of a family of p-ary linear codes constructed with defining set. The weight enumerator is an immediate result of the complete weight enumerator, which shows that the codes proposed in this paper are three-weight linear codes. Additionally, all nonzero codewords are minimal and thus they are suitable for secret sharing.

Keywords

Linear code Complete weight enumerator Gaussian period Gauss sum 

Mathematics Subject Classification

94B15 11T71 

Notes

Acknowledgments

The authors are very grateful to the editor and the anonymous reviewers for their helpful comments and suggestions, which have improved the presentation of this paper. The work of Zheng-An Yao is partially supported by the NSFC (Grant No. 11271381), the NSFC (Grant No. 11431015) and China 973 Program (Grant No. 2011CB808000). This work is also partially supported by the NSFC (Grant No. 61472457) and Guangdong Natural Science Foundation (Grant No. 2014A030313161).

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of MathematicsSun Yat-sen UniversityGuangzhouPeople’s Republic of China
  2. 2.School of Mathematical SciencesQufu Normal UniversityShandongPeople’s Republic of China

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