Designs, Codes and Cryptography

, Volume 86, Issue 5, pp 1007–1022 | Cite as

Four classes of linear codes from cyclotomic cosets



This paper presents four classes of linear codes from coset representatives of subgroups and cyclotomic coset families of certain finite field, and determines their weight enumerators. These linear codes may have applications in consumer electronics, communications and secret sharing schemes.


Linear code Cyclic code Weight distribution Gauss sum 

Mathematics Subject Classification

11T71 94B15 



The authors wish to thank prof. Qing Xiang for his helpful comments. The work was partially supported by National Natural Science Foundation of China (NSFC) under Grant 11101131.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and StatisticsHubei UniversityWuhanChina
  2. 2.Department of MathematicsNingbo UniversityNingboChina

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