A specific type of permutation and complete permutation polynomials over finite fields


Ongan P., GÜLMEZ TEMÜR B.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.19, no.4, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 4
  • Publication Date: 2020
  • Doi Number: 10.1142/s021949882050067x
  • Title of Journal : JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Abstract

In this paper, we study polynomials of the form f(x) = x (qn-1/q-1+1) + bx is an element of F-qn[x], where n = 5 and list all permutation polynomials (PPs) and complete permutation polynomials (CPPs) of this form. This type of polynomials were studied by Bassalygo and Zinoviev for the cases n = 2 and n = 3, Wu, Li, Helleseth and Zhang for the case n = 4, p not equal 2, Bassalygo and Zinoviev answered the question for the case n = 4, p= 2 and finally by Bartoli et al. for the case n = 6. Here, we determine all PPs and CPPs for the case n = 5.