Maximal Binary Cliques

In the paper we investigate the class of maximal, with respect to inclusion, binary k-cliques, that is subsets C of the hypercube n{0,1} such that for each two different x,y∈C the Hamming distance between x and y is some constant k, see [Sloane, N.J.A., Unsolved Problems in Graph Theory Arising from the Study Codes, Graph Theory Notes of New York, 18 (1989), 11–20]. We give a full classification of maximal binary 2-cliques and we determine precisely the cardinality of the set of all maximal binary 2-cliques.