On some combinatorial properties of propagation criteria for Boolean functions

In this paper we consider the issues of synthesis and analysis of parameterized classes of Boolean functions, which are asymptotically good with respect to the propagation criterion. The design of such classes of Boolean functions is based on the construction proposed by A. Bernasconi and B. Codenotti, using the bipartite Cayley graph of a Boolean function. We present a constructive description of classes of Boolean functions that are asymptotically good with respect to the propagation criterion. We investigate the basic properties of such classes and obtain lower estimates of their cardinalities.