Geodesic
Completely regular codes in the $n$-dimensional rectangular grid
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 861-869

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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. 
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     author = {S. V. Avgustinovich and A. Yu. Vasil'eva},
     title = {Completely regular codes in the $n$-dimensional rectangular grid},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {861--869},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a35/}
}
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S. V. Avgustinovich; A. Yu. Vasil'eva. Completely regular codes in the $n$-dimensional rectangular grid. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 19 (2022) no. 2, pp. 861-869. http://geodesic.mathdoc.fr/item/SEMR_2022_19_2_a35/