COMPLETELY REGULAR CODES IN THE n-DIMENSIONAL RECTANGULAR GRID

被引：1

作者：

Avgustinovich, S., V ^{[1
]}

Vasil'eva, A. Yu ^{[1
,2
]}

机构：

[1] Sobolev Inst Math, Pr Koptyuga 4, Novosibirsk 630090, Russia

[2] Novosibirsk State Univ, Pirogova Str 1, Novosibirsk 630090, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2022年 / 19卷 / 02期

关键词：

n-dimensional rectangular grid; completely regular code; intersection array; covering radius; perfect coloring;

D O I：

10.33048/semi.2022.19.072

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：861 / 869

页数：9

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