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

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.