4.4 Article

A general construction of permutation polynomials of Fq2

Journal

FINITE FIELDS AND THEIR APPLICATIONS
Volume 89, Issue -, Pages -

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.ffa.2023.102193

Keywords

Finite field; Permutation polynomial; Self -dual polynomial

Ask authors/readers for more resources

A general construction is provided to generate permutation polynomials of Fq2 with certain properties, including previously unknown polynomials. This construction is particularly suitable for permutation binomials and trinomials.
Let r be a positive integer, h(X) is an element of Fq2 [X], and mu q+1 be the subgroup of order q + 1 of Fq*2. It is well known that Xrh(Xq-1) permutes Fq2 if and only if gcd(r, q - 1) = 1 and Xrh(X)q-1 permutes mu q+1. There are many ad hoc constructions of permutation polynomials of Fq2 of this type such that h(X)q-1 induces monomial functions on the cosets of a subgroup of mu q+1. We give a general construction that can generate, through an algorithm, all permutation polynomials of Fq2 with this property, including many which are not known previously. The construction is illustrated explicitly for permutation binomials and trinomials.(c) 2023 Elsevier Inc. All rights reserved.

Authors

I am an author on this paper
Click your name to claim this paper and add it to your profile.

Reviews

Primary Rating

4.4
Not enough ratings

Secondary Ratings

Novelty
-
Significance
-
Scientific rigor
-
Rate this paper

Recommended

No Data Available
No Data Available