Permutation polynomials over finite fields have been studied extensively recently due to their wide applications in cryptography, coding theory, communication theory, among others. Recently, several authors have studied permutation trinomials of the form xh ( x ) over Fq2 , where q = 2 , h(x) = 1+x+x and r, s, t, k > 0 are integers. Their methods are essentially usage of a multiplicative versio...

We give a simple condition for a linear recurrence (mod 2W) of degree r to have the maximal possible period 2M_1(2'' 1). It follows that the period is maximal in the cases of interest for pseudorandom number generation, i.e., for three-term linear recurrences defined by trinomials which are primitive (mod 2) and of degree r > 2 . We consider the enumeration of certain exceptional polynomials wh...