On permutation polynomials over finite fields: differences and iterations

Nurdagül Anbar Meidl, Almasa Odzak, Vandita Patel, Luciane Quoos, Anna Somoza, Alev Topuzoglu

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Abstract

The Carlitz rank of a permutation polynomial f over a finite field Fq is a simple concept that was introduced in the last decade. Classifying permutations over Fq
with respect to their Carlitz ranks has some advantages, for instance f with a given Carlitz rank can be approximated by a rational linear transformation. In this note we present our recent results on the permutation behaviour of polynomials f+g, where f is a permutation over Fq of a given Carlitz rank, and g ∈ Fq[x] is of prescribed degree. We describe the relation of this problem to the well-known Chowla-Zassenhaus conjecture. We also study iterations of permutation polynomials by using the approximation property that is mentioned above.
Original languageEnglish
Title of host publicationWomen in Numbers
Number of pages13
Publication date2017
Publication statusPublished - 2017

Bibliographical note

conference paper submitted to Women in Numbers Europe

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