Danyao Wu , Pingzhi Yuan , Huanhuan Guan , Juan Li
{"title":"有限域上三类置换多项式的合成逆","authors":"Danyao Wu , Pingzhi Yuan , Huanhuan Guan , Juan Li","doi":"10.1016/j.ffa.2024.102523","DOIUrl":null,"url":null,"abstract":"<div><div>R. Gupta, P. Gahlyan and R.K. Sharma presented three classes of permutation trinomials over <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></msub></math></span> in Finite Fields and Their Applications. In this paper, we employ the local method to prove that those polynomials are indeed permutation polynomials and provide their compositional inverses.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"101 ","pages":"Article 102523"},"PeriodicalIF":1.2000,"publicationDate":"2024-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The compositional inverses of three classes of permutation polynomials over finite fields\",\"authors\":\"Danyao Wu , Pingzhi Yuan , Huanhuan Guan , Juan Li\",\"doi\":\"10.1016/j.ffa.2024.102523\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>R. Gupta, P. Gahlyan and R.K. Sharma presented three classes of permutation trinomials over <span><math><msub><mrow><mi>F</mi></mrow><mrow><msup><mrow><mi>q</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></msub></math></span> in Finite Fields and Their Applications. In this paper, we employ the local method to prove that those polynomials are indeed permutation polynomials and provide their compositional inverses.</div></div>\",\"PeriodicalId\":50446,\"journal\":{\"name\":\"Finite Fields and Their Applications\",\"volume\":\"101 \",\"pages\":\"Article 102523\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-10-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Finite Fields and Their Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S107157972400162X\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Finite Fields and Their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S107157972400162X","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
The compositional inverses of three classes of permutation polynomials over finite fields
R. Gupta, P. Gahlyan and R.K. Sharma presented three classes of permutation trinomials over in Finite Fields and Their Applications. In this paper, we employ the local method to prove that those polynomials are indeed permutation polynomials and provide their compositional inverses.
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.