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Quasi-cyclic Goppa codes with special Goppa polynomials and matched location sets

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Abstract

The paper considers a new subclass of quasi-cyclic Goppa codes having special Goppa polynomial \(G(x)=x^{q^{l}+1}+ax^{q^{l}}+a^{q^{m}}bx+b, a \notin \{M \cup \{-M\}\}, b \in M=\{\alpha : \alpha ^{q^{m}}=\alpha ^{-1}, \alpha \in GF(q^{2m})\}\), where q is a prime number. For this subclass, improved lower bounds for the dimension and the minimum distance are obtained. It is shown that this subclass contains the best known and optimal codes.

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Acknowledgments

The authors would like to thank Prof. Thierry P. Berger and the referees for their helpful comments and suggestions that improved the presentation of this paper.

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Authors and Affiliations

  1. Saint Petersburg State University of Aerospace Instrumentation, 67, Bolshaya Morskaya st., 190000, St. Petersburg, Russia

    Sergey Bezzateev & Natalia Shekhunova

Authors
  1. Sergey Bezzateev
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  2. Natalia Shekhunova
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Corresponding author

Correspondence to Sergey Bezzateev.

Additional information

The research leading to these results has received funding from the Ministry of Education and Science of the Russian Federation according to the project part of the state funding assignment No 2.2716.2014/K, July 17th, 2014.

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Bezzateev, S., Shekhunova, N. Quasi-cyclic Goppa codes with special Goppa polynomials and matched location sets. Cryptogr. Commun. 9, 23–39 (2017). https://doi.org/10.1007/s12095-016-0196-3

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  • DOI: https://doi.org/10.1007/s12095-016-0196-3

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