English
 
Help Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
  Full classification of permutation rational functions and complete rational functions of degree three over finite fields

Ferraguti, A., & Micheli, G. (2020). Full classification of permutation rational functions and complete rational functions of degree three over finite fields. Designs, Codes and Cryptography, 88(5), 867-886. doi:10.1007/s10623-020-00715-0.

Item is

Files

show Files
hide Files
:
arXiv:1805.03097.pdf (Preprint), 258KB
Name:
arXiv:1805.03097.pdf
Description:
File downloaded from arXiv at 2020-06-26 13:37
OA-Status:
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
:
Ferraguti-Micheli_Full classification of permutation rational functions and complete rational functions of degree three over finite fields_2020.pdf (Publisher version), 361KB
 
File Permalink:
-
Name:
Ferraguti-Micheli_Full classification of permutation rational functions and complete rational functions of degree three over finite fields_2020.pdf
Description:
-
OA-Status:
Visibility:
Restricted ( Max Planck Society (every institute); )
MIME-Type / Checksum:
application/pdf
Technical Metadata:
Copyright Date:
-
Copyright Info:
-
License:
-

Locators

show
hide
Locator:
https://doi.org/10.1007/s10623-020-00715-0 (Publisher version)
Description:
-
OA-Status:

Creators

show
hide
 Creators:
Ferraguti, Andrea1, Author           
Micheli, Giacomo, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

Content

show
hide
Free keywords: Mathematics, Number Theory, Computer Science, Cryptography and Security, Discrete Mathematics
 Abstract: Let $q$ be a prime power, $\mathbb F_q$ be the finite field of order $q$ and
$\mathbb F_q(x)$ be the field of rational functions over $\mathbb F_q$. In this
paper we classify all rational functions $\varphi\in \mathbb F_q(x)$ of degree
3 that induce a permutation of $\mathbb P^1(\mathbb F_q)$. Our methods are
constructive and the classification is explicit: we provide equations for the
coefficients of the rational functions using Galois theoretical methods and
Chebotarev Density Theorem for global function fields. As a corollary, we
obtain that a permutation rational function of degree 3 permutes $\mathbb F_q$
if and only if it permutes infinitely many of its extension fields. As another
corollary, we derive the well-known classification of permutation polynomials
of degree 3. As a consequence of our classification, we can also show that
there is no complete permutation rational function of degree $3$ unless $3\mid
q$ and $\varphi$ is a polynomial.

Details

show
hide
Language(s): eng - English
 Dates: 2020
 Publication Status: Issued
 Pages: 20
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Degree: -

Event

show

Legal Case

show

Project information

show

Source 1

show
hide
Title: Designs, Codes and Cryptography
  Abbreviation : Des. Codes Cryptogr.
Source Genre: Journal
 Creator(s):
Affiliations:
Publ. Info: Springer
Pages: - Volume / Issue: 88 (5) Sequence Number: - Start / End Page: 867 - 886 Identifier: -