Special orthogonal matrices: existence, enumeration and applications

我的研究主要集中在Hadamard矩阵及其应用方面。我们有没有想过，从非常远的距离拍摄的图片是如何传输的？我们从其他星球上看到的高质量彩色图像是使用非常复杂的基于数学的技术传输的。任何以数字方式传输的数据都容易出错。为了最大限度地减少误差，数据在传输之前被编码，在检索之后被解码。类似的技术被用于在CD和DVD上存储数据。*阿达玛矩阵在理论和实践中提供了最好的编码和解码技术。不过，关于Hadamard矩阵还有很多需要学习和发现的地方。例如，量子技术带来的预期计算革命在一定程度上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，我们努力成为这一努力的一部分。

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.