Some skew constacyclic codes over \(\mathbb {F}_{q}+u\mathbb {F}_{q}\)

Abstract

In this paper, we give conditions on the existence of Euclidean self-dual skew cyclic and skew negacyclic codes over the finite chain ring \(\mathbb {F}_q+u\mathbb {F}_q\). We also extend an algorithm of Boucher and Ulmer [J. Symbolic Comput. 60, 2014] to construct self-dual skew cyclic and skew negacyclic codes based on the least common left multiples of non-commutative polynomials over \(\mathbb {F}_q+u\mathbb {F}_q\). Furthermore, we give conditions on the existence of LCD skew cyclic and skew negacyclic codes. Detailed examples are given which were obtained with the aid of the Magma Computational Algebra System Bosma et al. (J Symbolic Comput 24(3–4):235–265, 1997).

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Acknowledgements

The authors are greatly indebted to the editor and reviewers for their remarks and advice which allowed us to improve the paper considerably.

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Correspondence to K. Guenda.

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Communicated by Eduardo Souza de Cursi.

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Hebbache, Z., Guenda, K., Özzaim, N.T. et al. Some skew constacyclic codes over \(\mathbb {F}_{q}+u\mathbb {F}_{q}\). Comp. Appl. Math. 40, 52 (2021). https://doi.org/10.1007/s40314-021-01425-6

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Keywords

  • Finite chain ring
  • Skew polynomial ring
  • Self-dual skew codes
  • Complexity
  • LCD skew codes

Mathematics Subject Classification

  • 94B05
  • 94B15
  • 94B6