The (non-)existence of perfect codes in Fibonacci cubes

The Fibonacci cube ? n is obtained from the n-cube Q n by removing all the vertices that contain two consecutive 1s. It is proved that ? n admits a perfect code if and only if n ? 3 . Fibonacci cubes are isometric subgraphs of hypercubes and form an appealing model for interconnection networks.The study of codes in graphs presents a wide generalization of the problem of the existence of classical error-correcting codes.In this paper, it is proved that Fibonacci cubes do not admit any perfect code, unless the dimension is less than or equal to 3.

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