Construction of perfectly balanced functions without barriers

From the results of the previous papers dedicated to the set of perfectly balanced Boolean functions, one can conclude that the subset of Boolean functions without barriers is of prior interest in this set. Such a subset was considered previously, and the nonemptiness of it was proven, but no nontrivial estimations of the cardinality of this subset were found. In the current paper, some methods for constructing perfectly balanced Boolean functions without barriers are considered. They are based on the composition of Boolean functions of a special form and on certain important properties of such composition.