The Existence of a Class of Balanced Multi-output Rotation Symmetric Boolean Functions

A new characterization of balanced rotation symmetric (n,m)-functions is presented. Based on the characterization, the nonexistence of balanced rotation symmetric (p^r, m)-functions is determined, where p is an odd prime and m ≥ 2. And there exist balanced rotation symmetric (2^r, m)-functions for 2 ≤ m ≤ 2^r-r. With the help of these results, we also prove that there exist rotation symmetric resilient (2^r, m)-functions for 2 ≤ m ≤ 2^r-r-1.