Some classes of permutation pentanomials

IF 1.2 3区 数学 Q1 MATHEMATICS
Zhiguo Ding , Michael E. Zieve
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引用次数: 0

Abstract

For each prime p3 and each power q=pk, we present two large classes of permutation polynomials over Fq2 of the form XrB(Xq1) which have at most five terms, where B(X) is a polynomial with coefficients in {1,1}. The special case p=2 of our results comprises a vast generalization of 76 recent results and conjectures in the literature. In case p>2, no instances of our permutation polynomials have appeared in the literature, and the construction of such polynomials had been posed as an open problem. Our proofs are short and involve no computations, in contrast to the proofs of many of the special cases of our results which were published previously.
几类置换五反常项
对于每一个素数p≠3和每一个幂q=pk,我们给出了Fq2上的两大类排列多项式,其形式为XrB(Xq−1),最多有五项,其中B(X)是系数为{1,−1}的多项式。我们的结果的特殊情况p=2包含了文献中76个最近的结果和猜想的广泛概括。在情况p>;2中,没有我们的排列多项式的实例出现在文献中,并且这种多项式的构造已被作为一个开放问题提出。我们的证明很短,不涉及计算,与之前发表的我们的结果的许多特殊情况的证明相反。
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来源期刊
CiteScore
2.00
自引率
20.00%
发文量
133
审稿时长
6-12 weeks
期刊介绍: Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.
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