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Assuming the existence of a partition in perfect codes of the vertex set of a finite or infinite bipartite graph G we give the construction of a perfect code in the Cartesian product G G P 2 . Such a partition is easily obtained in the case of perfect codes in Abelian Cayley graphs and we give some examples of applications of this result and its generalizations.doi:10.1016/j.ejc.2010.11.007 fatcat:anltxzft7nepbfteifospozkve