Permutation polynomials of the type $$x^rg(x^{s})$$ x r g ( x s ) over $${\mathbb {F}}_{q^{2n}}$$ F q 2 n

Permutation polynomials of the type $$x^rg(x^{s})$$ x r g ( x s ) over $${\mathbb... We provide some new families of permutation polynomials of $${\mathbb {F}}_{q^{2n}}$$ F q 2 n of the type $$x^rg(x^{s})$$ x r g ( x s ) , where the integers r, s and the polynomial $$g \in {\mathbb {F}}_q[x]$$ g ∈ F q [ x ] satisfy particular restrictions. Some generalizations of known permutation binomials and trinomials that involve a sort of symmetric polynomials are given. Other constructions are based on the study of algebraic curves associated to certain polynomials. In particular we generalize families of permutation polynomials constructed by Gupta–Sharma, Li–Helleseth, Li–Qu–Li–Fu. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Designs, Codes and Cryptography Springer Journals

Permutation polynomials of the type $$x^rg(x^{s})$$ x r g ( x s ) over $${\mathbb {F}}_{q^{2n}}$$ F q 2 n

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media, LLC
Subject
Mathematics; Combinatorics; Coding and Information Theory; Data Structures, Cryptology and Information Theory; Data Encryption; Discrete Mathematics in Computer Science; Information and Communication, Circuits
ISSN
0925-1022
eISSN
1573-7586
D.O.I.
10.1007/s10623-017-0415-8
Publisher site
See Article on Publisher Site

Abstract

We provide some new families of permutation polynomials of $${\mathbb {F}}_{q^{2n}}$$ F q 2 n of the type $$x^rg(x^{s})$$ x r g ( x s ) , where the integers r, s and the polynomial $$g \in {\mathbb {F}}_q[x]$$ g ∈ F q [ x ] satisfy particular restrictions. Some generalizations of known permutation binomials and trinomials that involve a sort of symmetric polynomials are given. Other constructions are based on the study of algebraic curves associated to certain polynomials. In particular we generalize families of permutation polynomials constructed by Gupta–Sharma, Li–Helleseth, Li–Qu–Li–Fu.

Journal

Designs, Codes and CryptographySpringer Journals

Published: Sep 20, 2017

References

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