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Dihedral Codes with Prescribed Minimum Distance

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Arithmetic of Finite Fields (WAIFI 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12542))

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Abstract

Dihedral codes, particular cases of quasi-cyclic codes, have a nice algebraic structure which allows to store them efficiently. In this paper, we investigate it and prove some lower bounds on their dimension and minimum distance, in analogy with the theory of BCH codes. This allows us to construct dihedral codes with prescribed minimum distance. In the binary case, we present some examples of optimal dihedral codes obtained by this construction.

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Acknowledgements

The authors are grateful to G.N. Alfarano, P. Moree and A. Neri for the fruitful discussion about the paper. Moreover, they would like to thank all reviewers for their insightful comments which led to an improvement of the paper.

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Authors and Affiliations

  1. Université Paris 8, Laboratoire de Géométrie, Analyse et Applications, LAGA, Université Sorbonne Paris Nord, CNRS, UMR 7539, 93430, Villetaneuse, France

    Martino Borello

  2. Faculty of Mathematics, University of Sciences and Technology Houari Boumediene, Algiers, Algeria

    Abdelillah Jamous

Authors
  1. Martino Borello
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  2. Abdelillah Jamous
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Correspondence to Martino Borello .

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Editors and Affiliations

  1. Sorbonne Paris, Paris, France

    Jean Claude Bajard

  2. Sabancı University, Istanbul, Turkey

    Alev Topuzoğlu

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Borello, M., Jamous, A. (2021). Dihedral Codes with Prescribed Minimum Distance. In: Bajard, J.C., Topuzoğlu, A. (eds) Arithmetic of Finite Fields. WAIFI 2020. Lecture Notes in Computer Science(), vol 12542. Springer, Cham. https://doi.org/10.1007/978-3-030-68869-1_8

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  • DOI: https://doi.org/10.1007/978-3-030-68869-1_8

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