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Configurations Maximizing the Number of Pairs of Hamming‐Adjacent Lattice Points

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The following question is considered: Which sets of k lattice points among the nd points in a d‐dimensional cube of length n maximize the number of pairs of points differing in only one coordinate? It is shown that maximal configurations for any (d, n, k) are obtained by choosing the first k points in a lexicographic ordering of the points by coordinates. Some possible generalizations of the problem are discussed.
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Document Type: Research Article

Affiliations: 1: Massachusetts Institute of Technology 2: University of California, Los Angeles

Publication date: June 1, 1971

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