To the theory of qq-ary Steiner and other-type trades

We introduce the concept of a clique bitrade, which generalizes several known types of bitrades, including latin bitrades, Steiner T(k−1,k,v) bitrades, extended 1-perfect bitrades. For a distance-regular graph, we show a one-to-one correspondence between the clique bitrades that meet the weight-distribution lower bound on the cardinality and the bipartite isometric subgraphs that are distance-regular with certain parameters. As an application of the results, we find the minimum cardinality of qq-ary Steiner Tq(k−1,k,v) bitrades and show a connection of minimum such bitrades with dual polar subgraphs of the Grassmann graph Jq(v,k)Jq(v,k).