一种具有分层局部性的最大可恢复码的新构造

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-07-07 DOI:10.1016/j.ffa.2025.102686

Rajendra Prasad Rajpurohit, Maheshanand Bhaintwal

{"title":"一种具有分层局部性的最大可恢复码的新构造","authors":"Rajendra Prasad Rajpurohit, Maheshanand Bhaintwal","doi":"10.1016/j.ffa.2025.102686","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper, we present a novel construction of maximally recoverable codes with two-level hierarchical locality using a parity-check matrix approach. The construction given in this paper utilizes Gabidulin codes for mid-level heavy parities and linearized Reed-Solomon codes for global heavy parities. When the number of local sets is small, this construction performs better than the previously known constructions as the field size required in our construction is smaller for such cases, making it useful for practical scenarios in distributed data storage systems. We also consider a special case of our construction when the number of global parities is fixed and is equal to 1. In this case, our construction performs better when the number of local sets is small and the number of mid-level parities is even.</div></div>","PeriodicalId":50446,"journal":{"name":"Finite Fields and Their Applications","volume":"109 ","pages":"Article 102686"},"PeriodicalIF":1.2000,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A new construction of maximally recoverable codes with hierarchical locality\",\"authors\":\"Rajendra Prasad Rajpurohit, Maheshanand Bhaintwal\",\"doi\":\"10.1016/j.ffa.2025.102686\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>In this paper, we present a novel construction of maximally recoverable codes with two-level hierarchical locality using a parity-check matrix approach. The construction given in this paper utilizes Gabidulin codes for mid-level heavy parities and linearized Reed-Solomon codes for global heavy parities. When the number of local sets is small, this construction performs better than the previously known constructions as the field size required in our construction is smaller for such cases, making it useful for practical scenarios in distributed data storage systems. We also consider a special case of our construction when the number of global parities is fixed and is equal to 1. In this case, our construction performs better when the number of local sets is small and the number of mid-level parities is even.</div></div>\",\"PeriodicalId\":50446,\"journal\":{\"name\":\"Finite Fields and Their Applications\",\"volume\":\"109 \",\"pages\":\"Article 102686\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2025-07-07\",\"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/S1071579725001169\",\"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/S1071579725001169","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

本文利用奇偶校验矩阵的方法，提出了一种具有两级分层局部性的最大可恢复码的构造方法。本文给出的构造方法使用Gabidulin码表示中级重偶，线性化Reed-Solomon码表示全局重偶。当局部集的数量很少时，这种构造比以前已知的构造表现得更好，因为在这种情况下，我们的构造所需的字段大小更小，这使得它对分布式数据存储系统中的实际场景很有用。我们还考虑了我们的构造的一个特殊情况，即全局奇偶的数量是固定的并且等于1。在这种情况下，我们的构造在局部集的数量较少且中级奇偶的数量为偶数时表现更好。

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

A new construction of maximally recoverable codes with hierarchical locality

In this paper, we present a novel construction of maximally recoverable codes with two-level hierarchical locality using a parity-check matrix approach. The construction given in this paper utilizes Gabidulin codes for mid-level heavy parities and linearized Reed-Solomon codes for global heavy parities. When the number of local sets is small, this construction performs better than the previously known constructions as the field size required in our construction is smaller for such cases, making it useful for practical scenarios in distributed data storage systems. We also consider a special case of our construction when the number of global parities is fixed and is equal to 1. In this case, our construction performs better when the number of local sets is small and the number of mid-level parities is even.

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

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.