Janez Žerovnik (Author)

Abstract

Let ▫$G = \times^n_{i=1}C_{\ell_i}$▫ be a direct product of cycles. It is known that for any ▫$r \le 1$▫, and any ▫$n \le 2▫$, each connected component of ▫$G$▫ contains a so-called canonical ▫$r$▫-perfect code provided that each ▫$\ell_i$▫ is a multiple of ▫$r^n + (r+1)^n$▫. Here we prove that up to a reasonably defined equivalence, these are the only perfect codes that exist.

Keywords

matematika;teorija grafov;korekcijske kode;direktni produkt grafov;popolne kode;cikli;mathematics;graph theory;error-correcting codes;direct product of graphs;perfect codes;cycles;

Data

Language: English
Year of publishing:
Typology: 1.01 - Original Scientific Article
Organization: UM FS - Faculty of Mechanical Engineering
UDC: 519.17
COBISS: 14621785 Link will open in a new window
ISSN: 0196-8858
Views: 1111
Downloads: 78
Average score: 0 (0 votes)
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Other data

Secondary language: Unknown
Secondary keywords: matematika;teorija grafov;korekcijske kode;direktni produkt grafov;popolne kode;cikli;
URN: URN:SI:UM:
Type (COBISS): Not categorized
Pages: 197-205
Volume: ǂVol. ǂ41
Issue: ǂiss. ǂ2
Chronology: 2008
DOI: 10.1016/j.aam.2007.04.006
ID: 1473502