Construction and Count of 1-Resilient Rotation Symmetric Boolean Functions on p^r Variables

Construction and count of 1-resilient Rotation symmetric Boolean functions (RSBFs) on p^r variables are demonstrated. It is proved that constructions of 1-resilient RSBFs on p^r variables are equivalent to solving an equation system. An accurate enumeration formula of all 1-resilient RSBFs on p^r variables is also proposed. Some examples are given, and the exact numbers of 1-resilient RSBFs on 8 and 9 variables are obtained respectively.