New results on permutation binomials of finite fields
New results on permutation binomials of finite fields
复制标题
有限域置换二项式的新结果
DOI：
10.1016/j.ffa.2023.102179
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发表时间：
2023
影响因子：
1
通讯作者：
Pallozzi Lavorante, Vincenzo
中科院分区：
文献类型：
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作者：
Hou, Xiang-dong;Pallozzi Lavorante, Vincenzo
在简要回顾了有限域上置换二项式的现有结果之后，我们引入了置换二项式之间等价的概念，并描述了在等价下如何使置换二项式达到其标准形。然后我们集中讨论形式为Xn(Xd(Q−1)+a)的FQ2的∈⁎，其中n和d是正整数。我们的贡献包括两个不存在的结果：(1)如果Q是偶数且充分大且是Q+1≠1，则Xn(X3(Q−1)+a)不是FQ2的PB。(2)如果2≤d|q+1，Q充分大且是Q+1≠1，则在某些附加条件下，Xn(Xd(Q−1)+a)不是FQ2的PB.(1)部分证实了Tu等人最近的一个猜想.(2)当n=1时，推广了前人的结果.
After a brief review of the existing results on permutation binomials of finite fields, we introduce the notion of equivalence among permutation binomials (PBs) and describe how to bring a PB to its canonical form under equivalence. We then focus on PBs of F q 2 of the form X n (X d (q− 1)+ a), where n and d are positive integers and a∈ F q 2⁎. Our contributions include two nonexistence results:(1) If q is even and sufficiently large and a q+ 1≠ 1, then X n (X 3 (q− 1)+ a) is not a PB of F q 2.(2) If 2≤ d| q+ 1, q is sufficiently large and a q+ 1≠ 1, then X n (X d (q− 1)+ a) is not a PB of F q 2 under certain additional conditions.(1) partially confirms a recent conjecture by Tu et al.(2) is an extension of a previous result with n= 1.
具有偶特征的有限域上的二项式排列
DOI：
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发表时间：
2021
期刊：
Designs, Codes and Cryptography
影响因子：
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作者：
Ziran Tu;Xiangyong Zeng;Yupeng Jiang;Yan Li
通讯作者：
Yan Li