Codes on Algebraic Curves

代数曲线代码

• 批准号: 8719626
• 负责人: P. Vijay Kumar
• 金额: $ 11.5万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-09-01 至 1991-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8719626&HistoricalAwards=false
• 关键词: Codes; Algebraic; Curves

The principle investigator (PI) proposes to investigate topics concerned with the recent application of algebraic geometry to error-correcting codes--work that showed the existence of a sequence of error-correcting codes that have performance exceeding the previously known Gilbert-Varshamov bound. Specifically the PI will attempt to construct codes using varieties of higher dimension such as surfaces, explicitly describe codes on modular curves, investigate methods of constructing codes having prescribed symmetries using the automorphism group of the underlying curve, and explore efficient decoding algorithms for codes on curves of genus greater than zero.

首席研究员 (PI) 提议研究与最近代数几何在纠错码中的应用有关的主题，该工作表明存在一系列纠错码，其性能超过了先前已知的 Gilbert-Varshamov 界限。 具体来说，PI将尝试使用各种更高维度（例如曲面）构造代码，显式描述模曲线上的代码，研究使用基础曲线的自同构群构造具有规定对称性的代码的方法，并探索曲线上代码的有效解码算法大于零的属。