Cyclic decomposition of permutations of finite fields obtained using monomials

Abstract

In this paper we study permutations of finite fields Fq that decompose as products of cycles of the same length, and are obtained using monomials cursive Greek chii ∈ Fq [cursive Greek chi]. We give the necessary and sufficient conditions on the exponent i to obtain such permutations. We also present formulas for counting the number of this type of permutations. An application to the construction of encoders for turbo codes is also discussed. © Springer-Verlag Berlin Heidelberg 2004.