Semidefinite programming bounds for few-distance sets in the Hamming and Johnson spaces

06/27/2022

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by   Alexander Barg, et al.

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We study the maximum cardinality problem of a set of few distances in the Hamming and Johnson spaces. We formulate semidefinite programs for this problem and extend the 2011 works by Barg-Musin and Musin-Nozaki. As our main result, we find new parameters for which the maximum size of two- and three-distance sets is known exactly.