Further results on permutation polynomials of the form \((x^{p^m}-x+\delta)^s+x\) over \(\mathbb{F}_{p^{2m}}\)

DOI10.1016/j.ffa.2017.11.011zbMath1400.11155OpenAlexW2773351447MaRDI QIDQ1696756

Rohit Gupta, Rajendra K. Sharma

Publication date: 15 February 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.2017.11.011

zbMATH Keywords

finite fieldpermutation polynomialtrace function

Mathematics Subject Classification ID

Polynomials over finite fields (11T06)

Related Items (10)

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 \(\mathbb{F}_{q^2}\) ⋮ General constructions of permutation polynomials of the form \((x^{2^m} + x + \delta)^{i(2^m - 1) + 1} + x\) over \(\mathbb{F}_{2^{2 m}}\) ⋮ Complete permutation polynomials with the form \((x^{p^m} - x + \delta)^s + a x^{p^m} + b x\) over \(\mathbb{F}_{p^n}\) ⋮ Some results on complete permutation polynomials and mutually orthogonal Latin squares ⋮ Two types of permutation polynomials with special forms ⋮ Two classes of permutation trinomials with Niho exponents over finite fields with even characteristic ⋮ Extended framework for constructing (complete) permutations by specifying their coordinate functions ⋮ Determination of a type of permutation binomials and trinomials ⋮ Further results on permutation trinomials with Niho exponents ⋮ Regular complete permutation polynomials over \(\mathbb{F}_{2^n} \)

Cites Work

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• Two classes of permutation polynomials having the form \((x^{2^m}+x+\delta)^s+x\)
• Permutation polynomials from piecewise functions
• Permutation polynomials over finite fields from a powerful lemma
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• A family of skew Hadamard difference sets
• Permutation polynomials and applications to coding theory
• 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 \(m\).
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• 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
• 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 \(\mathbb F_{2^m}\)
• Permutation polynomials over finite fields -- a survey of recent advances
• Further results on permutation polynomials of the form (xpm − x + δ)s + L(x) over 𝔽p2m
• Permutation Polynomials in RSA-Cryptosystems
• Optimal Ternary Cyclic Codes From Monomials
• Two classes of permutation polynomials over finite fields

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