在 $$\mathbb {F}_{q^n}$ 上具有迹函数的稀疏置换多项式的新结果

IF 0.6 4区工程技术 Q4 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Applicable Algebra in Engineering Communication and Computing Pub Date : 2024-05-13 DOI:10.1007/s00200-024-00658-2

Yan-Ping Wang, Zhengbang Zha

{"title":"在 $$\\mathbb {F}_{q^n}$ 上具有迹函数的稀疏置换多项式的新结果","authors":"Yan-Ping Wang, Zhengbang Zha","doi":"10.1007/s00200-024-00658-2","DOIUrl":null,"url":null,"abstract":"Permutation polynomials with sparse forms over finite fields attract researchers’ great interest and have important applications in many areas of mathematics and engineering. In this paper, by investigating the exponents (s, i) and the coefficients \$a,b\\in \\mathbb {F}_{q}^{*}\$, we present some new results of permutation polynomials of the form \$f(x)= ax^{q^i(q^{2}-q+1)} + bx^{s} + \\textrm{Tr}_{q^n/q}(x)\$ over \$\\mathbb {F}_{q^n}\$ (\$n=2\$ or 3). The permutation property of the new results is given by studying the number of solutions of special equations over \$\\mathbb {F}_{q^n}\$.","PeriodicalId":50742,"journal":{"name":"Applicable Algebra in Engineering Communication and Computing","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"New results of sparse permutation polynomials with trace functions over $$\\\\mathbb {F}_{q^n}$$\",\"authors\":\"Yan-Ping Wang, Zhengbang Zha\",\"doi\":\"10.1007/s00200-024-00658-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Permutation polynomials with sparse forms over finite fields attract researchers’ great interest and have important applications in many areas of mathematics and engineering. In this paper, by investigating the exponents (s, i) and the coefficients \\\$a,b\\\\in \\\\mathbb {F}_{q}^{*}\\\$, we present some new results of permutation polynomials of the form \\\$f(x)= ax^{q^i(q^{2}-q+1)} + bx^{s} + \\\\textrm{Tr}_{q^n/q}(x)\\\$ over \\\$\\\\mathbb {F}_{q^n}\\\$ (\\\$n=2\\\$ or 3). The permutation property of the new results is given by studying the number of solutions of special equations over \\\$\\\\mathbb {F}_{q^n}\\\$.\",\"PeriodicalId\":50742,\"journal\":{\"name\":\"Applicable Algebra in Engineering Communication and Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applicable Algebra in Engineering Communication and Computing\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1007/s00200-024-00658-2\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Algebra in Engineering Communication and Computing","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1007/s00200-024-00658-2","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

摘要

有限域上具有稀疏形式的置换多项式引起了研究人员的极大兴趣，并在数学和工程的许多领域有着重要的应用。本文通过研究指数 (s, i) 和系数 $a,b\in \mathbb {F}_{q}^{*}$、我们提出了形式为 $f(x)= ax^{q^i(q^{2}-q+1)} + bx^{s} + \textrm{Tr}_{q^n/q}(x)$ over $\mathbb {F}_{q^n}$ ($n=2$ or 3) 的置换多项式的一些新结果。通过研究特殊方程在 $\mathbb {F}_{q^n}$ 上的解的个数，可以给出新结果的置换性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

New results of sparse permutation polynomials with trace functions over $$\mathbb {F}_{q^n}$$

Permutation polynomials with sparse forms over finite fields attract researchers’ great interest and have important applications in many areas of mathematics and engineering. In this paper, by investigating the exponents (s, i) and the coefficients $a,b\in \mathbb {F}_{q}^{*}$, we present some new results of permutation polynomials of the form $f(x)= ax^{q^i(q^{2}-q+1)} + bx^{s} + \textrm{Tr}_{q^n/q}(x)$ over $\mathbb {F}_{q^n}$ ($n=2$ or 3). The permutation property of the new results is given by studying the number of solutions of special equations over $\mathbb {F}_{q^n}$.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applicable Algebra in Engineering Communication and Computing 工程技术-计算机：跨学科应用

CiteScore

2.90

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Algebra is a common language for many scientific domains. In developing this language mathematicians prove theorems and design methods which demonstrate the applicability of algebra. Using this language scientists in many fields find algebra indispensable to create methods, techniques and tools to solve their specific problems. Applicable Algebra in Engineering, Communication and Computing will publish mathematically rigorous, original research papers reporting on algebraic methods and techniques relevant to all domains concerned with computers, intelligent systems and communications. Its scope includes, but is not limited to, vision, robotics, system design, fault tolerance and dependability of systems, VLSI technology, signal processing, signal theory, coding, error control techniques, cryptography, protocol specification, networks, software engineering, arithmetics, algorithms, complexity, computer algebra, programming languages, logic and functional programming, algebraic specification, term rewriting systems, theorem proving, graphics, modeling, knowledge engineering, expert systems, and artificial intelligence methodology. Purely theoretical papers will not primarily be sought, but papers dealing with problems in such domains as commutative or non-commutative algebra, group theory, field theory, or real algebraic geometry, which are of interest for applications in the above mentioned fields are relevant for this journal. On the practical side, technology and know-how transfer papers from engineering which either stimulate or illustrate research in applicable algebra are within the scope of the journal.