Standard

Completely regular codes in the n-dimensional rectangular grid. / Avgustinovich, S. V.; Vasil'eva, A. Yu.

In: Siberian Electronic Mathematical Reports, Vol. 19, No. 2, 2022, p. 861-869.

Research output: Contribution to journal › Article › peer-review

Harvard

Avgustinovich, SV & Vasil'eva, AY 2022, 'Completely regular codes in the n-dimensional rectangular grid', Siberian Electronic Mathematical Reports, vol. 19, no. 2, pp. 861-869. https://doi.org/10.33048/semi.2022.19.072

APA

Avgustinovich, S. V., & Vasil'eva, A. Y. (2022). Completely regular codes in the n-dimensional rectangular grid. Siberian Electronic Mathematical Reports, 19(2), 861-869. https://doi.org/10.33048/semi.2022.19.072

Vancouver

Avgustinovich SV, Vasil'eva AY. Completely regular codes in the n-dimensional rectangular grid. Siberian Electronic Mathematical Reports. 2022;19(2):861-869. doi: 10.33048/semi.2022.19.072

Author

Avgustinovich, S. V. ; Vasil'eva, A. Yu. / Completely regular codes in the n-dimensional rectangular grid. In: Siberian Electronic Mathematical Reports. 2022 ; Vol. 19, No. 2. pp. 861-869.

BibTeX

@article{a0013a54b62e4bdd88795a3a5ba2026e,
title = "Completely regular codes in the n-dimensional rectangular grid",
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 = "Completely regular code, Covering radius, Intersection array, N-dimensional rectangular grid, Perfect coloring",
author = "Avgustinovich, {S. V.} and Vasil'eva, {A. Yu}",
year = "2022",
doi = "10.33048/semi.2022.19.072",
language = "English",
volume = "19",
pages = "861--869",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",
number = "2",

}

RIS

TY - JOUR

T1 - Completely regular codes in the n-dimensional rectangular grid

AU - Avgustinovich, S. V.

AU - Vasil'eva, A. Yu

PY - 2022

Y1 - 2022

N2 - 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.

AB - 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.

KW - Completely regular code

KW - Covering radius

KW - Intersection array

KW - N-dimensional rectangular grid

KW - Perfect coloring

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UR - https://www.elibrary.ru/item.asp?id=50336857

UR - https://www.mendeley.com/catalogue/39ee61f3-367e-30cc-9909-b946013af314/

U2 - 10.33048/semi.2022.19.072

DO - 10.33048/semi.2022.19.072

M3 - Article

VL - 19

SP - 861

EP - 869

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

IS - 2

ER -

ID: 45808293