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On the traveling salesman problem in binary Hamming spaces

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3 Author(s)
Cohen, G. ; ENST, Paris, France ; Litsyn, S. ; Zemor, G.

Given a subset X of vertices of the n-cube (i.e., the n-dimensional Hamming space), we are interested in the solution of the traveling salesman problem; namely, the minimal length of a cycle passing through all vertices of X. For a given number M, we estimate the maximum of these lengths when X ranges over all possible choices of sets of M vertices. Asymptotically, our estimates show that for a number M of vertices growing exponentially in n, the maximum is attained for a code with maximal possible minimum distance

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Information Theory, IEEE Transactions on  (Volume:42 ,  Issue: 4 )