Special orthogonal matrices: existence, enumeration and applications

特殊正交矩阵：存在性、枚举及应用

• 批准号: 104972-2013
• 负责人: Kharaghani, Hadi
• 金额: $ 1.09万
• 依托单位: University of Lethbridge
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=569032
• 关键词: Special; orthogonal; matrices; existence; enumeration

My research is mostly on Hadamard matrices and their applications. Did we ever wonder how pictures from a very long distance are transmitted? The high quality colour pictures that we have seen from other planets are transmitted using very sophisticated mathematically based technologies. Any digitally transmitted data is subject to errors. In order to minimize the errors, the data are coded before transmission and decoded after retrieval. Similar sort of technologies are used in storing data on CD's and DVD's. Hadamard matrices provide the best coding and decoding technique in theory and practice. There is much more to learn and discover about Hadamard matrices though. For example, the anticipated revolution in computing due to quantum technologies depends in part on a better understanding of the structure of Hadamard matrices. Together with my research collaborators we strive to be a part of this endeavor.

我的研究主要是阿达玛矩阵及其应用。我们有没有想过远距离的图像是如何传输的？我们从其他行星上看到的高质量彩色图像是使用非常复杂的数学技术传输的。任何数字传输的数据都可能出错。 为了使错误最小化，数据在传输之前被编码并且在检索之后被解码。类似的技术也用于在CD和DVD上存储数据。 Hadamard矩阵在理论和实践上提供了最好的编码和解码技术。然而，关于阿达玛矩阵还有很多东西需要学习和发现。例如，量子技术带来的计算革命部分取决于对阿达玛矩阵结构的更好理解。与我的研究合作者一起，我们努力成为这一奋进的一部分。