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

摘要

The following question is considered: Which sets ofklattice points among thendpoints in ad‐dimensional cube of lengthnmaximize 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 firstkpoints in a lexicographic ordering of the points by coordinates. Some possible generalizations of the problem are discusse