| Title: | An almost complete description of perfect codes in direct products of cycles |
|---|
| Authors: | ID Klavžar, Sandi (Author)
ID Špacapan, Simon (Author)
ID Žerovnik, Janez (Author) |
|---|
| Files: |  http://dx.doi.org/10.1016/j.aam.2005.10.002
|
|---|
| Language: | English |
|---|
| Work type: | Scientific work |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | PEF - Faculty of Education
|
|---|
| Abstract: | Let ▫$G = times_{i=1}^nC_{ell_i}$▫ be a direct product of cycles. It is proved that for any ▫$r ge 1$▫, and any ▫$n ge 2$▫, each connected component of ▫$G$▫ contains an ▫$r$▫-perfect code provided that each ▫$ell_i$▫ is a multiple of ▫$r^n + (r+1)^n▫$. On the other hand, if a code of ▫$G$▫ contains a given vertex and its canonical local vertices, then any ▫$ell_i$▫ is a multiple of ▫$r^n + (r+1)^n$▫. It is also proved that an ▫$r$▫-perfect code ▫$(r ge 2)$▫ of ▫$G$▫ is uniquely determined by ▫$n$▫ vertices, and it is conjectured that for ▫$r ge 2$▫ no other codes in ▫$G$▫ exist other than the constructed ones. |
|---|
| Keywords: | mathematics, graph theory, error-correcting codes, direct product of graphs, perfect codes, cycles |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publisher: | Elsevier |
|---|
| Year of publishing: | 2006 |
|---|
| Number of pages: | str. 2-18 |
|---|
| Numbering: | Letn. 37, št. 1 |
|---|
| PID: | 20.500.12556/DKUM-51554  |
|---|
| UDC: | 519.17 |
|---|
| ISSN on article: | 0196-8858 |
|---|
| COBISS.SI-ID: | 14026329 |
|---|
| NUK URN: | URN:SI:UM:DK:Q6ZZVSAS |
|---|
| Publication date in DKUM: | 10.07.2015 |
|---|
| Views: | 24348 |
|---|
| Downloads: | 105 |
|---|
| Metadata: |    |
|---|
| Categories: | Misc.
|
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
