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Partitions into Perfect Codes in the Hamming and Lee Metrics

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Abstract

We propose new combinatorial constructions of partitions into perfect codes in both the Hamming and Lee metrics. Also, we present a new combinatorial construction method for diameter perfect codes in the Lee metric, which is further developed to a construction of partitions into such codes. For the Lee metric, we improve previously known lower bounds on the number of perfect and diameter perfect codes proposed by Etzion in 2011.

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Funding

The research was carried out at the expense of the Russian Science Foundation, project no. 22-21-00135, https://rscf.ru/en/project/22-21-00135/

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 4 Acad. Koptyug Avenue, 630090, Novosibirsk, Russia

    F. I. Solov’eva

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  1. F. I. Solov’eva
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Translated from Problemy Peredachi Informatsii, 2022, Vol. 58, No. 3, pp. 58–69 https://doi.org/10.31857/S0555292322030056.

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Solov’eva, F. Partitions into Perfect Codes in the Hamming and Lee Metrics. Probl Inf Transm 58, 254–264 (2022). https://doi.org/10.1134/S003294602203005X

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  • DOI: https://doi.org/10.1134/S003294602203005X

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