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


Ongan P., GÜLMEZ TEMÜR B.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.19, sa.4, 2020 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Konu: 4
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1142/s021949882050067x
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Özet

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.