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DNA codes over \(GR(2^{3},d)[X]/\langle X^{2},2X \rangle\)

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Abstract

The main results of this paper are in two directions. First, the family of finite local rings of length 4 whose annihilator of their maximal ideals have length 2 is determined. Second, the structure of constacyclic, reversible and DNA codes over those rings are described, the length of the code is relatively prime to the characteristic of the residue field of the ring.

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Acknowledgements

The authors would like to thank the referees for their valuable observations and comments.

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Author notes

  1. C. Álvarez-García, C. A. Castillo-Guillén and Mohamed Badaoui have contributed equally to this work.

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma Metropolitana-I, San Rafael Atlixco Ave 186, 09340, México City, México

    C. Álvarez-García

  2. Instituto Politécnico Nacional , Escuela Superior de Ingeniería Mecánica y Eléctrica, Av. Luis Enrique Erro s/n, 07738, Ciudad de México, México

    C. A. Castillo-Guillén & Mohamed Badaoui

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  1. C. Álvarez-García
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  2. C. A. Castillo-Guillén
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  3. Mohamed Badaoui
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Correspondence to C. Álvarez-García.

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Álvarez-García, C., Castillo-Guillén, C.A. & Badaoui, M. DNA codes over \(GR(2^{3},d)[X]/\langle X^{2},2X \rangle\). AAECC (2024). https://doi.org/10.1007/s00200-024-00667-1

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  • DOI: https://doi.org/10.1007/s00200-024-00667-1

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