Codes from Curves: Structure, Decoding, and Modern Applications
曲线编码:结构、解码和现代应用
基本信息
- 批准号:1855136
- 负责人:
- 金额:$ 18万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2018
- 资助国家:美国
- 起止时间:2018-08-01 至 2023-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This award supports research into algebraic coding theory. The large volume of data generated today motivates the need for distributed storage systems which can provide long-term storage of data with highly reliable retrieval and availability of information to users. A distributed storage system consists of a network of storage nodes. A stored file may be retrieved by accessing these nodes. In such a system, individual nodes may be unreliable; for instance, they may become unavailable due to routine maintenance. For this reason, how information is stored across the network is highly relevant. The goal is to create a storage system that allows for recovery of lost data while limiting both network traffic and the number of disks accessed. This project addresses the problem by appealing to the underlying structure of a family of error-correcting codes defined using algebraic geometry. The codes have robust structure that yields powerful local properties and potential to balance storage overhead, reliability, network traffic, and repair bandwidth. This project considers the use of codes obtained via algebraic geometric constructions in highly relevant applications. The following problems will be studied: coding for distributed storage via algebraic geometric and combinatorial points of view, with the goals of minimizing node access and repair bandwidth; and explicit construction of locally correctable codes, quantum codes, and secret sharing schemes using algebraic geometric tools. Code structure will be explored, and decoding codes which are directs sum may be handled by decoding or repair within its factors. Full use will be made of the automorphism group of the code as well as natural nested structures inherited from the underlying algebraic geometry. Much of the work in this proposal is focused on algebraic geometric constructions utilized in situations where limiting network traffic in the decoding process is desirable; the aim is to accomplish this by capitalizing on the natural underlying structure of algebraic geometric codes rather than appealing exclusively to locality. In doing so, the performance guaranteed by the code construction is maintained (meaning code parameters do not suffer from local requirements) while making the codes more amenable to current applications.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
该奖项支持对代数编码理论的研究。今天生成的大量数据激发了对分布式存储系统的需求,该分布式存储系统可以为用户提供具有高度可靠的信息检索和可用性的数据的长期存储。分布式存储系统由存储节点网络组成。可以通过访问这些节点来检索存储的文件。在这样的系统中,单个节点可能是不可靠的;例如,它们可能由于日常维护而变得不可用。因此,信息如何在网络中存储非常重要。目标是创建一个存储系统,允许恢复丢失的数据,同时限制网络流量和访问的磁盘数量。这个项目解决了这个问题,呼吁使用代数几何定义的纠错码的家庭的底层结构。代码具有强大的结构,产生强大的本地属性和潜力,以平衡存储开销,可靠性,网络流量和修复带宽。 这个项目考虑了在高度相关的应用程序中使用通过代数几何结构获得的代码。将研究以下问题:通过代数几何和组合的角度来看,分布式存储的编码,以最小化节点访问和修复带宽的目标;和明确的本地可纠正的代码,量子码,和秘密共享计划的建设使用代数几何工具。对码的结构进行了探讨,对于直接和的译码码,可以在其因子内进行译码或修复。将充分利用代码的自同构群以及从底层代数几何继承的自然嵌套结构。在这个建议中的大部分工作都集中在代数几何结构中使用的情况下,限制网络流量的解码过程是可取的,目的是实现这一目标,利用代数几何代码的自然底层结构,而不是专门呼吁地方。这样,代码结构所保证的性能得以保持(这意味着代码参数不受当地要求的影响),同时使代码更适合当前的应用。该奖项反映了NSF的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。
项目成果
期刊论文数量(21)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Graph-based codes for hierarchical recovery
用于分层恢复的基于图的代码
- DOI:10.1109/isit50566.2022.9834902
- 发表时间:2022
- 期刊:
- 影响因子:0
- 作者:Beemer, Allison;Kshirsagar, Rutuja;Matthews, Gretchen L.
- 通讯作者:Matthews, Gretchen L.
Affine Cartesian codes with complementary duals
- DOI:10.1016/j.ffa.2019.01.004
- 发表时间:2018-05
- 期刊:
- 影响因子:0
- 作者:Hiram H. López;Felice Manganiello;Gretchen L. Matthews
- 通讯作者:Hiram H. López;Felice Manganiello;Gretchen L. Matthews
Norm-trace-lifted codes over binary fields
二进制字段上的范数跟踪提升代码
- DOI:10.1109/isit50566.2022.9834497
- 发表时间:2022
- 期刊:
- 影响因子:0
- 作者:Matthews, Gretchen L.;Murphy, Aidan W.
- 通讯作者:Murphy, Aidan W.
Erasures Repair for Decreasing Monomial-Cartesian and Augmented Reed-Muller Codes of High Rate
- DOI:10.1109/tit.2021.3130096
- 发表时间:2021-07
- 期刊:
- 影响因子:2.5
- 作者:H. L'opez;Gretchen L. Matthews;Daniel Valvo
- 通讯作者:H. L'opez;Gretchen L. Matthews;Daniel Valvo
Secure MatDot codes: a secure, distributed matrix multiplication scheme
- DOI:10.1109/itw54588.2022.9965839
- 发表时间:2022-11
- 期刊:
- 影响因子:0
- 作者:Hiram H. López;Gretchen L. Matthews;Daniel Valvo
- 通讯作者:Hiram H. López;Gretchen L. Matthews;Daniel Valvo
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Gretchen Matthews其他文献
Codes for distributed storage from 3-regular graphs
- DOI:
10.1016/j.dam.2017.04.014 - 发表时间:
2017-10-01 - 期刊:
- 影响因子:
- 作者:
Shuhong Gao;Fiona Knoll;Felice Manganiello;Gretchen Matthews - 通讯作者:
Gretchen Matthews
Cracking her codes: understanding shared technology resources as positioning artifacts for power and status in CSCL environments
- DOI:
10.1007/s11412-017-9261-y - 发表时间:
2017-09-01 - 期刊:
- 影响因子:5.700
- 作者:
Amber Simpson;Nicole Bannister;Gretchen Matthews - 通讯作者:
Gretchen Matthews
Gretchen Matthews的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Gretchen Matthews', 18)}}的其他基金
Collaborative Research: Evaluation Codes, Duals, and Applications
合作研究:评估代码、对偶和应用
- 批准号:
2201075 - 财政年份:2022
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
Collaborative Research: EAGER-QIA: High-Genus Code-Based Cryptography
合作研究:EAGER-QIA:基于高级代码的密码学
- 批准号:
2037833 - 财政年份:2020
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
Mathematics - Opportunities in Research and Education (MORE)
数学 - 研究和教育的机会(更多)
- 批准号:
1902214 - 财政年份:2019
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
Codes from Curves: Structure, Decoding, and Modern Applications
曲线编码:结构、解码和现代应用
- 批准号:
1802345 - 财政年份:2018
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
Algebraic analysis of parity check codes and iterative decoding
奇偶校验码的代数分析和迭代解码
- 批准号:
0901693 - 财政年份:2009
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
Applications of Semigroups to Algebraic Geometry Codes
半群在代数几何代码中的应用
- 批准号:
0201286 - 财政年份:2002
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
相似海外基金
CAREER: Quantifying Genetic and Ecological Constraints on the Evolution of Thermal Performance Curves
职业:量化热性能曲线演变的遗传和生态约束
- 批准号:
2337107 - 财政年份:2024
- 资助金额:
$ 18万 - 项目类别:
Continuing Grant
Euler Systems, Iwasawa Theory, and the Arithmetic of Elliptic Curves
欧拉系统、岩泽理论和椭圆曲线算术
- 批准号:
2401321 - 财政年份:2024
- 资助金额:
$ 18万 - 项目类别:
Continuing Grant
CAREER: Accelerating Algorithms for Computing Isogenies and Endomorphisms of Supersingular Elliptic Curves
职业:加速计算超奇异椭圆曲线同构和自同态的算法
- 批准号:
2340564 - 财政年份:2024
- 资助金额:
$ 18万 - 项目类别:
Continuing Grant
Combinatorics of Complex Curves and Surfaces
复杂曲线和曲面的组合
- 批准号:
2401104 - 财政年份:2024
- 资助金额:
$ 18万 - 项目类别:
Standard Grant
Super Quantum Curves and Super Voros Coefficients
超级量子曲线和超级 Voros 系数
- 批准号:
22KJ0715 - 财政年份:2023
- 资助金额:
$ 18万 - 项目类别:
Grant-in-Aid for JSPS Fellows
Random curves and surfaces with conformal symmetries
具有共形对称性的随机曲线和曲面
- 批准号:
2246820 - 财政年份:2023
- 资助金额:
$ 18万 - 项目类别:
Continuing Grant
The embedded topology of projective plane curves and the generalization of splitting invariants
射影平面曲线的嵌入拓扑和分裂不变量的推广
- 批准号:
23K03042 - 财政年份:2023
- 资助金额:
$ 18万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Study on supersingular curves and their moduli spaces via computational algebraic geometry and its applications to cryptography
基于计算代数几何的超奇异曲线及其模空间研究及其在密码学中的应用
- 批准号:
23K12949 - 财政年份:2023
- 资助金额:
$ 18万 - 项目类别:
Grant-in-Aid for Early-Career Scientists
Diversified study on Manin's conjecture for rational points/rational curves/motives
马宁有理点/有理曲线/动机猜想的多元化研究
- 批准号:
23H01067 - 财政年份:2023
- 资助金额:
$ 18万 - 项目类别:
Grant-in-Aid for Scientific Research (B)
Conference: 1, 2, 3: Curves, Surfaces, and 3-Manifolds
会议:1,2,3:曲线、曲面和 3-流形
- 批准号:
2246832 - 财政年份:2023
- 资助金额:
$ 18万 - 项目类别:
Standard Grant