Classification of permutation polynomials of the form $$x^3g(x^{q-1})$$ of $${\mathbb F}_{q^2}$$ where $$g(x)=x^3+bx+c$$ and $$b,c \in {\mathbb F}

Classification of permutation polynomials of the form $$x^3g(x^{q-1})$$ of $${\mathbb F}_{q^2}$$ where $$g(x)=x^3+bx+c$$ and $$b,c \in {\mathbb F}_q^*$$

Published:2022-05-22 Issue:7 Volume:90 Page:1537-1556
ISSN:0925-1022
Container-title:Designs, Codes and Cryptography
language:en
Short-container-title:Des. Codes Cryptogr.

Author:

Özbudak Ferruh^ORCID,Gülmez Temür Burcu

Funder

metu

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computer Science Applications

Link

https://link.springer.com/content/pdf/10.1007/s10623-022-01052-0.pdf

Reference35 articles.

1. Akbary A., Wang Q.: On polynomials of the form $$x^rf(x^{(q-1)/l})$$, Int. J. Math. Math. Sci. 7 (2007).

2. Aubry Y., McGuire G., Rodier F.: A few more functions that are not APN infinitely often. In: Finite Fields: Theory and Applications, Contemp. Math., vol. 518, pp. 23–31. Amer. Math. Soc., Providence (2010).

3. Bartoli D., Quoos L.: Permutation polynomials of the type $$x^rg(x^s)$$ over $${\mathbb{F}}_{q^{2n}}$$. Des. Codes Cryptogr. 86, 1589–1599 (2018).

4. Bartoli D.: On a conjecture about a class of permutation trinomials. Finite Fields Appl. 52, 30–50 (2018).

5. Bartoli D., Giulietti M.: Permutation polynomials, fractional polynomials, and algebraic curves. Finite Fields Appl. 51, 1–16 (2018).

Cited by 9 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On a class of permutation trinomials over finite fields;Turkish Journal of Mathematics;2024-07-03

2. Complete characterization of a class of permutation trinomials in characteristic five;Cryptography and Communications;2024-02-21

3. Several classes of permutation pentanomials with the form xrh(xpm−1) over Fp2m;Finite Fields and Their Applications;2023-12

4. Classification of some permutation quadrinomials from self reciprocal polynomials over F2n;Finite Fields and Their Applications;2023-10

5. On a class of permutation quadrinomials;Journal of Algebra and Its Applications;2023-09-22