Classification of Boolean Functions where Affine Functions are Uniformly Distributed

Classification of Non-linear Boolean functions is a long-standing problem in the area of theoreticalcomputer science. In this paper, effort has been made to achieve a systematic classification of all n-variableBoolean functions, where only one affine Boolean function belongs to each class. Two different methods areproposed to achieve this classification. The first method is a recursive procedure that uses the Cartesian productof sets starting from the set of 1-variable Boolean function and in the second method classification is achievedthrough a set of invariant bit positions with respect to an affine function belonging to that class. The invariant bitpositions also provide information concerning the size and symmetry properties of the classes/sub-classes, suchthat the members of classes/sub-classes satisfy certain similar properties.