On null completely regular codes in Manhattan metric Full article
| Journal |
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports)
, E-ISSN: 1813-3304 |
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| Output data | Year: 2025, Volume: 22, Number: 2, Pages: 1311-1333 Pages count : 23 DOI: 10.33048/semi.2025.22.079 | ||
| Tags | completely regular code, perfect coloring, infinite rectangular grid, Manhattan metric, Hamming metric | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | FWNF-2022-0017 |
Abstract:
We investigate the class of completely regular codes in graphs with a distance partition $C_0, \ldots, C_{\rho}$, where each set $C_i$, for $0 \leq i \leq s - 1$, is an independent set. This work focuses on the existence problem for such codes in the $n$-dimensional infinite grid. We demonstrate that several parameter families of such codes necessarily arise from binary or ternary Hamming graphs or do not exist. Furthermore, employing binary linear programming tech\-niques, we explore completely regular codes in infinite grids of dimensions $3$ and $4$ for the cases $s = 1$ and $s = 2$.
Cite:
Mogilnykh I.Y.
, Vasil'eva A.Y.
On null completely regular codes in Manhattan metric
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N2. P.1311-1333. DOI: 10.33048/semi.2025.22.079
On null completely regular codes in Manhattan metric
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2025. V.22. N2. P.1311-1333. DOI: 10.33048/semi.2025.22.079
Dates:
| Submitted: | May 13, 2025 |
| Accepted: | Sep 6, 2025 |
| Published print: | Nov 14, 2025 |
| Published online: | Nov 14, 2025 |
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