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On the cycle index and the weight enumerator

  • Tsuyoshi Miezaki
  • Manabu Oura
Article

Abstract

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.”

Keywords

Cycle index Complete weight enumerator 

Mathematics Subject Classification

Primary 11T71 Secondary 20B05 11H71 

Notes

Acknowledgements

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

References

  1. 1.
    Bannai E., Dougherty S.T., Harada M., Oura M.: Type II codes, even unimodular lattices and invariant rings. IEEE Trans. Inf. Theory 45, 257–269 (1999).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Cameron P.J.: Cycle index, weight enumerator, and Tutte polynomial. Electron. J. Comb. 9(1), 1 (2002).MathSciNetzbMATHGoogle Scholar
  3. 3.
    Cameron P.J.: Polynomial aspects of codes, matroids and permutation groups. http://www.maths.qmul.ac.uk/~pjc/csgnotes/cmpgpoly.pdf
  4. 4.
    Dougherty S.T., Gulliver T.A., Oura M.: Higher weights and graded rings for binary self-dual codes. Discret. Appl. Math. 128(1), 121–143 (2003).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Dougherty S.T., Gulliver T.A., Oura M.: Higher weights for ternary and quaternary self-dual codes. Des. Codes Cryptogr. 38(1), 97–112 (2006).MathSciNetCrossRefzbMATHGoogle Scholar

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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