Novel computational paradigms for combinatorial matrices

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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.