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A characterization of all semiprimitive irreducible cyclic codes in terms of their lengths

  • Gerardo VegaEmail author
Original Paper
  • 11 Downloads

Abstract

Just by looking at the lengths of irreducible cyclic codes, we present a simple numerical characterization by which we can easily identify those codes that are either one-weight or semiprimitive two-weight irreducible cyclic codes over any finite field. We then particularize our characterization to the class of irreducible cyclic codes of dimension two, and with this, we show that regardless of the finite field any code in this class is always either a one-weight or a semiprimitive two-weight irreducible cyclic code. We also explore the weight distribution of another kind of irreducible cyclic codes and present an infinite family comprising two subfamilies of irreducible cyclic codes that were recently studied.

Keywords

Irreducible cyclic codes Semiprimitive codes Weight distribution 

Notes

Acknowledgements

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

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

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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