Several classes of permutation pentanomials with the form xrh(xp) over Fp - Details

author：

Liu, Q. (Liu, Q..) ^[1] | Chen, G. (Chen, G..) ^[2] | Liu, X. (Liu, X..) ^[3] (Scholars：刘西蒙) | Zou, J. (Zou, J..) ^[4] (Scholars：邹剑)

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Abstract：

In　this　paper,　we　study　the　permutation　property　of　pentanomials　with　the　form　xrh(xp)　over　Fp,　where　p∈{2,3}.　More　precisely,　based　on　some　seventh-degree　and　eighth-degree　irreducible　pentanomials　over　F2,　we　present　eight　classes　of　permutation　pentanomials　over　F2　by　determining　the　solutions　of　some　equations　with　low　degrees.　In　addition,　based　on　the　investigation　of　algebraic　curves　associated　with　fractional　polynomials　over　finite　fields,　eight　classes　of　permutation　pentanomials　over　F3　are　discovered　by　choosing　some　seventh-degree　irreducible　pentanomials　over　F3.　Finally,　several　classes　of　permutation　pentanomials　and　heptanomials　over　F2　and　F3　are　derived　from　known　permutation　polynomials　on　μ2　and　μ3,　respectively,　where　μd　is　the　set　of　d-th　roots　of　unity.　©　2023　Elsevier　Inc.

Keyword：

Finite fields Permutation heptanomial Permutation pentanomial Permutation polynomial

Community：

[ 1 ] [Liu Q.]College of Computer and Data Science, Fuzhou University, Fuzhou, 350116, China
[ 2 ] [Liu Q.]Key Laboratory of Information Security of Network Systems, Fuzhou University, Fuzhou, 350116, China
[ 3 ] [Chen G.]College of Computer and Data Science, Fuzhou University, Fuzhou, 350116, China
[ 4 ] [Chen G.]Key Laboratory of Information Security of Network Systems, Fuzhou University, Fuzhou, 350116, China
[ 5 ] [Liu X.]College of Computer and Data Science, Fuzhou University, Fuzhou, 350116, China
[ 6 ] [Liu X.]Key Laboratory of Information Security of Network Systems, Fuzhou University, Fuzhou, 350116, China
[ 7 ] [Zou J.]College of Computer and Data Science, Fuzhou University, Fuzhou, 350116, China
[ 8 ] [Zou J.]Key Laboratory of Information Security of Network Systems, Fuzhou University, Fuzhou, 350116, China

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Source ：

Finite Fields and their Applications

ISSN： 1071-5797

Year： 2023

Volume： 92

1 . 2

JCR@2023

1 . 2 0 0

JCR@2023

JCR Journal Grade：1

CAS Journal Grade：3

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SCOPUS Cited Count： 1

ESI Highly Cited Papers on the List： 0 Unfold All

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