Classification of permutation polynomials of the form x3g(xq-1) of Fq2 where g(x) = x3+ bx+ c and b,c∈Fq∗

ÖZBUDAK F., Gülmez Temür B.

Designs, Codes, and Cryptography, vol.90, no.7, pp.1537-1556, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 90 Issue: 7
  • Publication Date: 2022
  • Doi Number: 10.1007/s10623-022-01052-0
  • Journal Name: Designs, Codes, and Cryptography
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, PASCAL, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH
  • Page Numbers: pp.1537-1556
  • Keywords: Finite fields, Permutation polynomials, Absolutely irreducible, FINITE-FIELDS, TRINOMIALS, BINOMIALS
  • Middle East Technical University Affiliated: Yes

Abstract

© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.We classify all permutation polynomials of the form x3g(xq-1) of Fq2 where g(x) = x3+ bx+ c and b,c∈Fq∗. Moreover we find new examples of permutation polynomials and we correct some contradictory statements in the recent literature. We assume that gcd (3 , q- 1) = 1 and we use a well known criterion due to Wan and Lidl, Park and Lee, Akbary and Wang, Wang, and Zieve.