On the cycle index and the weight enumerator

  • Tsuyoshi MiezakiEmail author
  • Manabu Oura


In this paper, we introduce the concept of the complete cycle index and discuss a relation with the complete weight enumerator in coding theory. This work was motivated by Cameron’s lecture notes “Polynomial aspects of codes, matroids and permutation groups.”


Cycle index Complete weight enumerator 

Mathematics Subject Classification

Primary 11T71 Secondary 20B05 11H71 



The authors would also like to thank the anonymous reviewers for their beneficial comments on an earlier version of the manuscript.


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Copyright information

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

Authors and Affiliations

  1. 1.Faculty of EducationUniversity of the RyukyusNishiharaJapan
  2. 2.Graduate School of Natural Science and TechnologyKanazawa UniversityKanazawaJapan

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