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On q-ary Codes with Two Distances d and d + 1

  • Coding Theory
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Abstract

We consider q-ary block codes with exactly two distances: d and d + 1. Several constructions of such codes are given. In the linear case, we show that all codes can be obtained by a simple modification of linear equidistant codes. Upper bounds for the maximum cardinality of such codes are derived. Tables of lower and upper bounds for small q and n are presented.

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Acknowledgement

We are grateful to a reviewer for detailed and insightful comments on the first version of this paper. We thank Grigory Kabatiansky for useful discussion concerning the codes under consideration.

Some research for this article was conducted while the first author was visiting the Department of Mathematical Sciences at Purdue University Fort Wayne.

Funding

The first author was partially supported by the National Scientific Program “Information and Communication Technologies for a Single Digital Market in Science, Education and Security” (ICTinSES) of the Bulgarian Ministry of Education and Science. The second author was supported by the National Program “Young Scientists and PostDocs” of the Bulgarian Ministry of Education and Science. The research of the third and forth authors was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Foundation for Basic Research (project no. 19-01-00364).

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Authors and Affiliations

  1. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    P. Boyvalenkov & K. Delchev

  2. Technical Faculty, South-Western University, Blagoevgrad, Bulgaria

    P. Boyvalenkov

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

    D. V. Zinoviev & V. A. Zinoviev

Authors
  1. P. Boyvalenkov
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  2. K. Delchev
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  3. D. V. Zinoviev
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  4. V. A. Zinoviev
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Corresponding authors

Correspondence to P. Boyvalenkov, K. Delchev, D. V. Zinoviev or V. A. Zinoviev.

Additional information

Russian Text © The Author(s), 2020, published in Problemy Peredachi Informatsii, 2020, Vol. 56, No. 1, pp. 38–50.

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Boyvalenkov, P., Delchev, K., Zinoviev, D.V. et al. On q-ary Codes with Two Distances d and d + 1. Probl Inf Transm 56, 33–44 (2020). https://doi.org/10.1134/S0032946020010044

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  • DOI: https://doi.org/10.1134/S0032946020010044

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