Permutation polynomials \((x^{p^m} - x + \delta)^{s_1} +(x^{p^m} - x + \delta)^{s_2} + x\) over \(\mathbb{F}_{p^n}\)

DOI10.1016/j.ffa.2018.01.003zbMath1385.05006OpenAlexW2793349312MaRDI QIDQ1747906

Lisha Li, Shi Wang, Xiangyong Zeng, Chaoyun Li

Publication date: 27 April 2018

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2018.01.003

zbMATH Keywords

finite fieldpermutation polynomialtrace functionAGW criterion

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Polynomials over finite fields (11T06) Arithmetic theory of polynomial rings over finite fields (11T55)

Related Items (15)

Some classes of permutation polynomials of the form \(b(x^q +ax+\delta)^{\frac{i(q^2 -1)}{d}+1}+c(x^q +ax+\delta)^{\frac{j(q^2 -1)}{d}+1}+L(x)\) over \(\mathbb{F}_{q^2}\) ⋮ New classes of complete permutation polynomials ⋮ Further results on permutation polynomials and complete permutation polynomials over finite fields ⋮ Necessary and sufficient conditions of two classes of permutation polynomials ⋮ Several classes of permutation polynomials of the form \((x^{p^m} - x + \delta)^s + x\) over \(\mathbb{F}_{p^{2m}}\) ⋮ Complete permutation polynomials with the form \((x^{p^m} - x + \delta)^s + a x^{p^m} + b x\) over \(\mathbb{F}_{p^n}\) ⋮ Several classes of permutation polynomials over the finite field \(\mathbb{F}_{p^{2 m}}\) ⋮ On inverses of some permutation polynomials over finite fields of characteristic three ⋮ Some results on complete permutation polynomials and mutually orthogonal Latin squares ⋮ Some new results on permutation polynomials of the form \(b (x^q + ax + \delta)^s - ax\) over \(\mathbb{F}_{q^2}\) ⋮ Several classes of permutation polynomials based on the AGW criterion over the finite field \(\mathbb{F}_{2^{2m}}\) ⋮ Two types of permutation polynomials with special forms ⋮ On a type of permutation rational functions over finite fields ⋮ Some new forms of permutation polynomials based on the AGW criterion ⋮ A link between two classes of permutation polynomials

Cites Work

• Some classes of permutation polynomials of the form \((x^{p^m}-x+\delta)^s+x\) over \(\mathbb{F}_{p^{2m}}\)
• Two classes of permutation polynomials having the form \((x^{2^m}+x+\delta)^s+x\)
• Permutation polynomials from piecewise functions
• On constructing permutations of finite fields
• Permutation polynomials over finite fields from a powerful lemma
• Further results on permutation polynomials of the form \((x^{p^m} - x + \delta)^s + L(x)\) over \(\mathbb{F}_{p^{2 m}}\)
• Two new permutation polynomials with the form \({\left(x^{2^k}+x+\delta\right)^{s}+x}\) over \({\mathbb{F}_{2^n}}\)
• New Kloosterman sums identities over \(\mathbb F_{2^m}\) for all \(m\).
• Further results on permutation polynomials over finite fields
• Permutation polynomials of the form \((x^{p^m} - x + \delta)^s + L(x)\) over the finite field \(\mathbb{F}_{p^{2 m}}\) of odd characteristic
• More classes of permutation polynomials of the form \((x^{p^m}-x+\delta)^s+L(x)\)
• Permutations via linear translators
• Permutation polynomials over \(\mathbb{F}_{2^n}\) of the form \((x^{2^i} + x + \delta)^{s_1} +(x^{2^i} + x + \delta)^{s_2} + x\)
• Permutation polynomials of the \((x^p - x+\delta)^s+L(x)\)
• Further results on a class of permutation polynomials over finite fields
• Four classes of permutation polynomials of \(\mathbb F_{2^m}\)
• Handbook of Finite Fields
• Two classes of permutation polynomials over finite fields

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