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Designs, Codes and Cryptography

, Volume 86, Issue 4, pp 835–840 | Cite as

A correction on the determination of the weight enumerator polynomial of some irreducible cyclic codes

  • Gerardo VegaEmail author
Article

Abstract

A classification that shows explicitly all possible weight enumerator polynomials for every irreducible cyclic code of length n over a finite field \(\mathbb {F}_q\), in the particular case where each prime divisor of n is also a divisor of \(q-1\), was recently given in Brochero Martínez and Giraldo Vergara (Des Codes Cryptogr 78:703–712, 2016). However, as we will see next, such classification is incomplete. Thus, the purpose of this work is to use an already known identity among the weight enumerator polynomials, in order to complete such classification. As we will see later, by means of this identity, we not only complete, in an easier way, this classification, but we also find out the nature of the weight distributions of the class of irreducible cyclic codes studied in Brochero Martínez and Giraldo Vergara (2016).

Keywords

Weight distribution Weight enumerator polynomial Irreducible cyclic codes 

Mathematics Subject Classification

94B15 11T71 

Notes

Acknowledgements

The author want to express his gratitude to the anonymous referees for their valuable suggestions.

References

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Dirección General de Cómputo y de Tecnologías de Información y ComunicaciónUniversidad Nacional Autónoma de MéxicoCiudad de MéxicoMexico

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