It is proved that the construction and enumeration of the number of balanced symmetric functions over GF (p) are equivalent to solving an equation system and enumerating the solutions. Furthermore, we give an lower bound on number of balanced symmetric functions over GF (p), and the lower bound provides best known results.

We introduce and discuss an algorithm using O(p) time and O(n(n + m)) space for enumerating the m > 0 chordless circuits in a digraph of order n and containing p chordless paths. Running it on random digraphs yields some statistical insight into its practical performance.