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Designs, Codes and Cryptography

, Volume 87, Issue 2–3, pp 317–325 | Cite as

The covering radii of a class of binary cyclic codes and some BCH codes

  • Selçuk Kavut
  • Seher TutdereEmail author
Article
  • 46 Downloads
Part of the following topical collections:
  1. Special Issue: Coding and Cryptography

Abstract

In 2003, Moreno and Castro proved that the covering radius of a class of primitive cyclic codes over the finite field \(\mathbb {F}_2\) having minimum distance 5 (resp. 7) is 3 (resp. 5). We here give a generalization of this result as follows: the covering radius of a class of primitive cyclic codes over \(\mathbb {F}_2\) with minimum distance greater than or equal to \(r+2\) is r, where r is any odd integer. Moreover, we prove that the primitive binary e-error correcting BCH codes of length \(2^f-1\) have covering radii \(2e-1\) for an improved lower bound of f.

Keywords

Cyclic code BCH code Covering radius Finite field Polynomial equations 

Mathematics Subject Classification

94B15 94B65 

Notes

Acknowledgements

This work is supported by the Project of Scientific Investigation (BAP 2015-A17), Gebze Technical University, Turkey.

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Copyright information

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

Authors and Affiliations

  1. 1.Department of Computer EngineeringBalıkesir UniversityBalıkesirTurkey
  2. 2.Department of MathematicsGebze Technical UniversityGebzeTurkey

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