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On the Classification of Completely Regular Codes with Covering Radius Two and Antipodal Duals

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Abstract

We classify all linear completely regular codes which have covering radius \(\rho=2\) and whose dual are antipodal. For this, we firstly show several properties of such dual codes, which are two-weight codes with weights \(d\) and \(n\).

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Funding

This work has been partially supported by the Spanish Ministerio de Ciencia e Innovación under Grant PID2022-137924NB-I00 (AEI/FEDER UE) and RED2022-134306-T, and by the Catalan AGAUR Grant 2021-SGR-00643. The research of the second and third authors of the paper was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences within the program of fundamental research on the topic “Mathematical Foundations of the Theory of Error-Correcting Codes” and was also supported by the National Science Foundation of Bulgaria under project no. 20-51-18002.

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Authors and Affiliations

  1. Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, Barcelona, Spain

    J. Borges

  2. Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences, Moscow, Russia

    V. A. Zinoviev & D. V. Zinoviev

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  1. J. Borges
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  2. V. A. Zinoviev
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  3. D. V. Zinoviev
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Correspondence to J. Borges.

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Borges, J., Zinoviev, V. & Zinoviev, D. On the Classification of Completely Regular Codes with Covering Radius Two and Antipodal Duals. Probl Inf Transm 59, 204–216 (2023). https://doi.org/10.1134/S003294602303002X

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