Perfect codes in direct products of cycles - a complete characterizationŽerovnik, Janez (Avtor) matematikateorija grafovkorekcijske kodedirektni produkt grafovpopolne kodeciklimathematicsgraph theoryerror-correcting codesdirect product of graphsperfect codescyclesLet ▫$G = times^n_{i=1}C_{ell_i}$▫ 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.20082015-07-10 15:01:38Delo ni kategorizirano51668sl