{"title":"Designs with a simple automorphism group","authors":"Alessandro Montinaro , Yanwei Zhao , Zhilin Zhang , Shenglin Zhou","doi":"10.1016/j.ffa.2024.102488","DOIUrl":null,"url":null,"abstract":"<div><p>The classification of the 2-designs with <span><math><mi>λ</mi><mo>=</mo><mn>2</mn></math></span> admitting a flag-transitive automorphism groups with socle <span><math><mi>P</mi><mi>S</mi><mi>L</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>q</mi><mo>)</mo></math></span> is completed by settling the two open cases in <span><span>[2]</span></span>. The result is achieved by using conics and hyperovals of <span><math><mi>P</mi><mi>G</mi><mo>(</mo><mn>2</mn><mo>,</mo><mi>q</mi><mo>)</mo></math></span>.</p></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"99 ","pages":"Article 102488"},"PeriodicalIF":1.2000,"publicationDate":"2024-08-09","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/S1071579724001278","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The classification of the 2-designs with admitting a flag-transitive automorphism groups with socle is completed by settling the two open cases in [2]. The result is achieved by using conics and hyperovals of .
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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