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里德该奖项支持南加州大学的欧文·S·里德教授和P.Vijay Kumar教授与博士后合作，与挪威卑尔根大学的Tor Helleseth教授和德国埃森大学的Henning Stichtenoth教授合作进行应用数学研究。总的来说，他们的研究领域是代数几何和编码理论之间的相互作用。他们合作的一个主要焦点是研究Galois环上的指数和，并将其应用于纠错码的设计和研究。另一个重要的组成部分涉及Grobner基技术，它们在有限域上的计算以及它们在循环和代数几何码的译码中的应用。为了补充美国组在纠错编码方面的优势，Helleseth教授贡献了代数函数论及其在编码理论中的应用方面的必要专业知识，以及Galois环和Grobner基的经验。他还提供了在挪威使用大规模并行计算机器的机会，这些机器将用于一些联合研究。斯蒂奇特诺斯教授是代数几何方面的专家，也是代数几何编码领域的世界领导者。他们的才能结合在一起，形成了一个极其强大的协作团队。这项研究是离散数学、符号计算和代数计算理论的交叉学科结合。这些结果将有助于指数和理论的进步，以及纠错码新的和改进的译码算法。这些结果将在数学、计算机科学和工程的几个领域中得到有用的应用。***