Algorithms in algebraic combinatorial design theory

代数组合设计理论中的算法

• 批准号: 249875-2006
• 负责人: Kotsireas, Ilias
• 金额: $ 1.09万
• 依托单位: Wilfrid Laurier University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2006
• 资助国家: 加拿大
• 起止时间: 2006-01-01 至 2007-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=338418
• 关键词: Algorithms; algebraic; combinatorial; design; theory

Combinatorial Designs are used in every day life, even though this is not always visible. Satellite transmissions use Error-correcting codes which are based on certain special kinds of combinatorial designs. Wireless communication protocols use combinatorial designs as well. The theory of combinatorial designs uses extensively tools from Mathematics (from areas such as Linear Algebra, Group Theory, Number Theory) and Computer Science (from areas such as Algorithms, High-performance computing, Metaheuristics). The main focus of our project is the study of combinatorial designs from a Computational Algebra point of view. Formalizing combinatorial designs via Computational  Algebra allows one to employ powerful techniques to study them. An important outcome of our project is the creation of databases with inequivalent designs. These databases are available to statisticians and other researchers.

组合设计在日常生活中使用，即使这并不总是可见的。卫星传输使用基于某些特殊类型的组合设计的纠错码。无线通信协议也使用组合设计。组合设计理论广泛使用数学（线性代数，群论，数论等领域）和计算机科学（算法，高性能计算，元分析等领域）的工具。我们项目的主要重点是从计算代数的角度研究组合设计。通过计算代数形式化组合设计允许人们采用强大的技术来研究它们。我们的项目的一个重要成果是创建具有不同设计的数据库。这些数据库可供统计人员和其他研究人员使用。