On inversive maximal period polynomials over finite fields

Over finite field GF(q) withq a power of an odd primep, we characterize inversive maximal period polynomials in terms of polynomials of orderq + 1, and then we study some properties of polynomials of orderq + 1.This paper was written while the author was visiting the Institute of Information Processing, Austrian Academy of Sciences, AustriaThe author would like to thank the Institute of Information Processing, Austrian Academy of Sciences, Austria, for its hospitality and for using its facilities