Novel computational paradigms for combinatorial matrices

我的建议是关于两个新的计算范式的应用到搜索组合矩阵的问题。这类矩阵在量子计算、统计学、编码理论、密码学、电信、数据/图像压缩、信息安全和其他领域都很普遍。这个提议背后的动机和想法来自于最近的一次成功，我与合作者一起为20年前两位工程师在文献中提出的一个问题提供了完整的解决方案。寻找新的组合矩阵的问题是非常困难的，在过去的几年里进展非常缓慢。许多不同的方法传统上已被用来寻找新的组合矩阵，似乎传统的技术已经达到饱和点。因此，寻找新的方法来解决这些问题是至关重要的，这也是我计划在未来五年的研究计划中要做的。

My proposal is concerned with the application of two novel computational paradigms into the problem of searching for combinatorial matrices. These kind of matrices are prevalent in quantum computing, statistics, coding theory, cryptography, telecommunications, data/image compression, information security and other areas. The motivations and ideas behind this proposal come from a recent success that I have had with collaborators in providing the complete solution to a problem that was proposed in the literature 20 years ago by two engineers. The problem of finding new combinatorial matrices is exceedingly difficult and progress over the last several years has been very slow. A number of different methodologies have been traditionally employed to find new combinatorial matrices and it seems that the traditional techniques have reached a point of saturation. Therefore it is essential to look at novel methods to apply to these problems and this is what I plan to do in my research program in the next five years.