A family of permutation trinomials over \(\mathbb{F}_{q^2}\)

DOI10.1016/j.ffa.2020.101781zbMath1472.11295arXiv1911.09526OpenAlexW3107426376MaRDI QIDQ1995216

Marco Timpanella, Daniele Bartoli

Publication date: 19 February 2021

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1911.09526

zbMATH Keywords

algebraic curvespermutation polynomials

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Polynomials over finite fields (11T06) Special polynomials in general fields (12E10)

Related Items (11)

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 \(b, c \in\mathbb{F}_q^*\) ⋮ Investigating rational perfect nonlinear functions ⋮ Complete characterization of some permutation polynomials of the form \(x^r (1+ax^{s_1(q-1)}+bx^{s_2(q-1)})\) over \(\mathbb{F}_{q^2}\) ⋮ Further results on a class of permutation trinomials ⋮ More classes of permutation hexanomials and pentanomials over finite fields with even characteristic ⋮ Constructing permutation polynomials over \(\mathbb{F}_{q^3}\) from bijections \(\mathrm{PG}(2,q)\) ⋮ Classification of some quadrinomials over finite fields of odd characteristic ⋮ On inverses of permutation polynomials of the form \(x(x^s-a)^{(q^m-1)/s}\) over \(\mathbb{F}_{q^n}\) ⋮ More constructions of \(n\)-cycle permutations ⋮ More classes of permutation quadrinomials from Niho exponents in characteristic two ⋮ More results about a class of quadrinomials over finite fields of odd characteristic

Uses Software

• Magma

Cites Work

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• Some new classes of permutation trinomials over finite fields with even characteristic
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• A class of new permutation trinomials
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• Full classification of permutation rational functions and complete rational functions of degree three over finite fields
• Determination of a class of permutation trinomials in characteristic three
• Several classes of permutation trinomials from Niho exponents
• Permutation polynomials and group permutation polynomials
• Permutation Trinomials Over Finite Fields with Even Characteristic
• On some permutation polynomials over $\mathbb {F}_q$ of the form $x^r h(x^{(q-1)/d})$
• Cyclotomic Mapping Permutation Polynomials over Finite Fields
• Two classes of permutation trinomials with Niho exponents

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