At most three-weight binary linear codes from generalized Moisio’s exponential sums

  • Yansheng Wu
  • Qin YueEmail author
  • Xueying Shi


In this paper, we evaluate two classes of new exponential sums, which are viewed as generalized Moisio’s exponential sums in contrast to the results by Heng and Yue (IEEE Commun Lett 19:1488–1491, 2015) and Moisio (Finite Fields Appl 15:644–651, 2009). As applications, we present two classes of binary linear codes with two wights or three weights. These codes can be used in secret sharing schemes and authentication codes.


Binary linear codes Gauss sums Gauss periods Secret sharing schemes 

Mathematics Subject Classification

11T71 11T24 



The paper is supported by National Natural Science Foundation of China (Nos. 61772015, 61602144, 11661013, 11661014), the Guangxi Natural Sciences Foundation (Nos. 2016GXNSFCA380014, 2016GXNSFDA380017), Foundation of Science and Technology on Information Assurance Laboratory (No. KJ-17-010), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (Nos. KYCX17_0225, KYCX18_0241), and the Fundamental Research Funds for the Central Universities (No. NZ2018005).


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Copyright information

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

Authors and Affiliations

  1. 1.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China
  2. 2.State Key Laboratory of CryptologyBeijingPeople’s Republic of China

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