{"title":"曲线上旗束的 AG 代码","authors":"Tohru Nakashima","doi":"10.1016/j.ffa.2024.102392","DOIUrl":null,"url":null,"abstract":"<div><p>In the present paper, we construct codes from the flag bundle associated to a vector bundle <em>E</em> over a curve. Our code may be considered as a relative version of the codes on the flag variety studied by F. Rodier. We investigate the dimension and the minimum distance of such relative Rodier codes using intersection theory. For this purpose, we exploit the invariants of vector bundles which control the asymptotic behavior of semistability of <em>E</em> under pull-back by Frobenius morphisms</p></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"AG codes on flag bundles over a curve\",\"authors\":\"Tohru Nakashima\",\"doi\":\"10.1016/j.ffa.2024.102392\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the present paper, we construct codes from the flag bundle associated to a vector bundle <em>E</em> over a curve. Our code may be considered as a relative version of the codes on the flag variety studied by F. Rodier. We investigate the dimension and the minimum distance of such relative Rodier codes using intersection theory. For this purpose, we exploit the invariants of vector bundles which control the asymptotic behavior of semistability of <em>E</em> under pull-back by Frobenius morphisms</p></div>\",\"PeriodicalId\":50446,\"journal\":{\"name\":\"Finite Fields and Their Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-02-22\",\"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/S1071579724000315\",\"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/S1071579724000315","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
摘要
在本文中，我们从与曲线上的向量束 E 相关联的旗形束中构造代码。我们的代码可以看作是罗迪尔（F. Rodier）所研究的旗上代码的相对版本。我们利用交集理论研究了这种相对罗迪尔码的维数和最小距离。为此，我们利用了向量束的不变量，这些不变量控制着 E 在弗罗贝纽斯态拉回下的半稳态性的渐近行为。
In the present paper, we construct codes from the flag bundle associated to a vector bundle E over a curve. Our code may be considered as a relative version of the codes on the flag variety studied by F. Rodier. We investigate the dimension and the minimum distance of such relative Rodier codes using intersection theory. For this purpose, we exploit the invariants of vector bundles which control the asymptotic behavior of semistability of E under pull-back by Frobenius morphisms
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
