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Quasi-cyclic codes: algebraic properties and applications

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Abstract

In this paper, we provide criteria for the reversibility and conjugate-reversibility of 1-generator quasi-cyclic codes. The Chinese remainder theorem is used to provide a characterization for generalized quasi-cyclic codes to be Galois linear complementary-dual and Galois self-dual. Using the approach proposed by Güneri and Özbudak (IEEE Trans Inf Theory 59(2):979–985, 2013), a new concatenated structure for quasi-cyclic codes is given. We show that Galois linear complementary-dual quasi-cyclic codes are asymptotically good over some finite fields. In addition, DNA codes are given which have more codewords than previously known codes.

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Authors and Affiliations

  1. Isfahan University of Technology, Isfahan, Iran

    Mohamadbagher Zeraatpisheh & Morteza Esmaeili

  2. University of Victoria, Victoria, Canada

    Morteza Esmaeili & T. Aaron Gulliver

Authors
  1. Mohamadbagher Zeraatpisheh
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  2. Morteza Esmaeili
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  3. T. Aaron Gulliver
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Correspondence to T. Aaron Gulliver.

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Communicated by Masaaki Harada.

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Zeraatpisheh, M., Esmaeili, M. & Gulliver, T.A. Quasi-cyclic codes: algebraic properties and applications. Comp. Appl. Math. 39, 96 (2020). https://doi.org/10.1007/s40314-020-1120-1

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  • DOI: https://doi.org/10.1007/s40314-020-1120-1

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