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On the cyclic order distribution and partitioning of linear cyclic codes

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Abstract

In this paper, we propose a way to partition any linear cyclic code in its cyclic equivalence classes according to the algebraic structure of the code. Such partition is useful to generate cyclically permutable codes directly from linear cyclic codes. We consider the case where the size of the finite field and the block length of the code are coprimes. Moreover, we present a criterion to construct maximal cyclic order codes.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Federal University of São João del-Rei, Minas Gerais, Brazil

    Gustavo Terra Bastos

  2. Department of Electronics and Systems, Federal University of Pernambuco, Recife, Brazil

    José Sampaio de Lemos-Neto

Authors
  1. Gustavo Terra Bastos
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  2. José Sampaio de Lemos-Neto
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Correspondence to Gustavo Terra Bastos.

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Communicated by Sergio R. López-Permouth.

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Bastos, G.T., Lemos-Neto, J.S.d. On the cyclic order distribution and partitioning of linear cyclic codes. São Paulo J. Math. Sci. 15, 404–418 (2021). https://doi.org/10.1007/s40863-020-00197-x

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  • DOI: https://doi.org/10.1007/s40863-020-00197-x

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