U.S.-Norway-Germany Cooperative Research: Some Problems in Galois Rings, Grobner Bases and their Applications (Applied Mathematics)

美国-挪威-德国合作研究：伽罗瓦环、格罗布纳基的一些问题及其应用（应用数学）

• 批准号: 9406614
• 负责人: Irving Reed
• 金额: $ 2.39万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-08-15 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9406614&HistoricalAwards=false
• 关键词: U.S.; Norway; Germany; Cooperative; Research

9406614 Reed This award supports Professors Irving S. Reed and P. Vijay Kumar of the University of Southern California, together with a postdoctoral associate, to collaborate in applied mathematics research with Professors Tor Helleseth of the University of Bergen, Norway, and Henning Stichtenoth of the University of Essen, Germany. In general, they are working in the area of the interaction between algebraic geometry and coding theory. A major focus of their collaboration is the study of exponential sums over Galois rings, and the application of this to the design and study of error correcting codes. Another significant component involves Grobner basis techniques, both their computation over finite fields and their application for the decoding of cyclic and algebraic-geometric codes. To complement the U.S. groups' strengths in error correcting codes, Professor Helleseth contributes necessary expertise in the theory of algebraic functions and their applications to coding theory as well as experience with Galois rings and Grobner bases. He also offers access to massively parallel computing machines in Norway which will be used for some of the joint research. Professor Stichtenoth is an expert on algebraic geometry and a world leader in the area of algebraic- geometric codes. The combination of their talents creates an extremely powerful collaborative team. The proposed research is an interdisciplinary combination of discrete mathematics, symbolic computation and algebraic computation theory. Results will contribute to advances in the theory of exponential sums and new and improved decoding algorithms for error-correcting codes. Such results will have useful applications in several fields of mathematics, computer science and engineering. ***

9406614 REED该奖项支持南加州大学的Irving S. Reed和P. Vijay Kumar教授，以及一位博士后合伙人，与卑尔根大学，挪威大学，挪威大学和埃森大学的Henning Stichtenoth的教授合作，与德国埃森大学的Henning Stichtenoth合作。 通常，它们在代数几何学和编码理论之间的相互作用领域工作。 他们协作的主要重点是研究Galois环的指数总和，以及该计划的应用在纠正误差代码的设计和研究中。 另一个重要组成部分涉及Grobner基碱基技术，包括对有限字段的计算以及它们用于解码环状和代数几何代码的应用。 为了补充美国团体在错误校正法规方面的优势，Heleseth教授在代数函数理论及其在编码理论中的应用以及与Galois Rings和Grobner基础的经验方面贡献了必要的专业知识。 他还提供了挪威大规模平行计算机的访问权限，该计算机将用于某些联合研究。 Stichtenoth教授是代数几何学的专家，并且是代数几何代码领域的世界领导者。 他们的才华的结合创造了一个非常有力的协作团队。 拟议的研究是离散数学，符号计算和代数计算理论的跨学科组合。 结果将有助于指数总和和新的和改进的解码算法的进步，以实现错误校正代码。 这些结果将在数学，计算机科学和工程的几个领域中具有有用的应用。 ***