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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2022, Volume 19, Issue 2, Pages 861–869
DOI: https://doi.org/10.33048/semi.2022.19.072 (Mi semr1545) 		 
Discrete mathematics and mathematical cybernetics

Completely regular codes in the $n$-dimensional rectangular grid

S. V. Avgustinovicha, A. Yu. Vasil'evaab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova str., 1, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/semi.2022.19.072
Abstract: It is proved that two sequences of the intersection array of an arbitrary completely regular code in the $n$-dimensional rectangular grid are monotonic. It is shown that the minimal distance of an arbitrary completely regular code is at most $4$ and the covering radius of an irreducible completely regular code in the grid is at most $2n$.
Keywords: $n$-dimensional rectangular grid, completely regular code, intersection array, covering radius, perfect coloring.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0017
The study was carried out within the framework of the state contract of the Sobolev Institute of Mathematics (project no. FWNF-2022-0017).
Received August 17, 2022, published November 11, 2022
Bibliographic databases:
Document Type: Article
UDC: 519.174.7, 519.725
MSC: 05C15, 05B40
Language: English
Citation: S. V. Avgustinovich, A. Yu. Vasil'eva, “Completely regular codes in the $n$-dimensional rectangular grid”, Sib. Èlektron. Mat. Izv., 19:2 (2022), 861–869
Citation in format AMSBIB
\Bibitem{AvgVas22}
\by S.~V.~Avgustinovich, A.~Yu.~Vasil'eva
\paper Completely regular codes in the $n$-dimensional rectangular grid
\jour Sib. \`Elektron. Mat. Izv.
\yr 2022
\vol 19
\issue 2
\pages 861--869
\mathnet{http://mi.mathnet.ru/semr1545}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=4508354}
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