Perfect codes in direct products of cycles—a complete characterization |
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Authors: | Janez
erovnik |
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Affiliation: | aUniversity of Maribor, FME, Smetanova 17, 2000 Maribor, Slovenia;bInstitute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia |
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Abstract: | Let be a direct product of cycles. It is known that for any r1, and any n2, each connected component of G contains a so-called canonical r-perfect code provided that each ℓi is a multiple of rn+(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: | Error-correcting codes Direct product of graphs Perfect codes Cycles |
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