Supplementary material Classification by Hierarchical Partitioning and Data dependent Grouping A Constant Weight Construction

In this supplement, we first describe two constant weight constructions, where each group has the same number of labels, and each label belongs to the same number of groups. The first construction we consider is based on LDPC (low density parity) codes. We consider this construction in our experiments. Framework For gROup testiNg) was proposed. The adjacency matrices corresponding to such graphs give us the desired constant weight constructions.