%0 Journal Article
%T Exponential sums and linear complexity of nonlinear pseudorandom number generators with polynomials of small $p$-weight degree
%A ¨˘lvar Ibeas
%A Arne Winterhof
%J Uniform Distribution Theory
%D 2010
%I Mathematical Institute of the Slovak Academy of Sciences
%X For a class of polynomials $f(X)$ of small $p$-weight degree over a finite field of characteristic $p$ we improve the general bounds on exponential sums and linear complexity of nonlinear pseudorandom number generators defined by $\mu_{n+1}= f(\mu_n), n=0,1,\ldots$ with some initial value $mu_0$. This extends the class of polynomials where a nontrivial exponential sum bound is known. From the bound on exponential sums we derive discrepancy bounds for nonlinear pseudorandom vectors.
%K Finite fields
%K pseudorandom numbers
%K discrepancy
%K exponential sums
%U http://www.boku.ac.at/MATH/udt/vol05/no1/6IbeWint10-1.pdf