On properties of pseudoboolean functions

For the class of pseudoboolean functions, the concepts of linear structures and the nonzeros' affine localization of a function in a binary vector space, its (strong) affine splittability, and algebraic degeneracy are introduced in analogy to the Boolean case. The interconnection of the main parameters characterizing these notions for an arbitrary pseudoboolean function, its Fourier transform, and its autocorrelation function is shown. The invariance of some of the parameters with respect to the action of a group, sometimes called the general affine group of transformations, on the set of pseudoboolean functions is also considered.