| Title: | Perfect codes in direct products of cycles - a complete characterization |
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| Authors: | ID Žerovnik, Janez (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.aam.2007.04.006
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FS - Faculty of Mechanical Engineering
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| 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. |
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| 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 |
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| Year of publishing: | 2008 |
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| Number of pages: | 197-205 |
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| Numbering: | Vol. 41, iss. 2 |
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| PID: | 20.500.12556/DKUM-51668  |
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| UDC: | 519.17 |
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| ISSN on article: | 0196-8858 |
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| COBISS.SI-ID: | 14621785 |
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| DOI: | 10.1016/j.aam.2007.04.006 |
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| NUK URN: | URN:SI:UM:DK:QRZ00PYR |
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| Publication date in DKUM: | 10.07.2015 |
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| Views: | 2129 |
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| Downloads: | 96 |
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| Metadata: |    |
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| Categories: | Misc.
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