指标q的置换多项式 + 1 / Fq2

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2026-06-01 Epub Date: 2026-01-19 DOI:10.1016/j.ffa.2026.102796

Xiutao Feng , Qiang Wang

引用次数: 0

摘要

从Fq的任意排列多项式出发，给出了Fq2上索引为q+1的排列多项式的一般构造。我们还使用系数在Fq2中的多项式扩展了我们的构造，使得它们在Fq2的一个子集上内射，该子集对应于所有(q+1)-单位根的集合μq+1。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Permutation polynomials of index q + 1 over Fq2

We provide a generic construction of permutation polynomials over

F_{q^{2}}

with index

q + 1

from any permutation polynomial of

F_{q}

. We also extend our construction using polynomials with coefficients in

F_{q^{2}}

such that they are injective over a subset of

F_{q^{2}}^{⁎}

, which corresponds to the set

μ_{q + 1}

of all

(q + 1)

-th roots of unity.

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来源期刊

Finite Fields and Their Applications 数学-数学

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.

指标q的置换多项式 + 1 / Fq2

摘要

指标q的置换多项式 + 1 / Fq2