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

Date

2022-07-01

Author

Özbudak, Ferruh
Gülmez Temür, Burcu

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© 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.

Subject Keywords

Absolutely irreducible, Finite fields, Permutation polynomials

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85130380578&origin=inward
https://hdl.handle.net/11511/98275

Journal

Designs, Codes, and Cryptography

DOI

https://doi.org/10.1007/s10623-022-01052-0

Collections

Department of Mathematics, Article

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Citation Formats

F. Özbudak and B. Gülmez Temür, “Classification of permutation polynomials of the form x3g(xq-1) of Fq2 where g(x) = x3+ bx+ c and b,c∈Fq∗,” Designs, Codes, and Cryptography, vol. 90, no. 7, pp. 1537–1556, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85130380578&origin=inward.