Algebraic Methods for Signal Processing and Communications Coding

the long version

The primary purpose of this monograph is to explore the ties between digital signal processing and error-control codes, with the thought of eventually making them two components of a unified theory, or of making a large part of the theory of error-control codes a subset of digital signal processing. By studying the properties of the Fourier transform in an arbitrary field, a perspective emerges in which the two subjects are unified. Because there are many fields and many Fourier transforms in most of these fields, the unified view will also uncover a rich set of mathematical tools, many of which have yet to find an engineering application. The author has published several well-known books, and is widely respected. The topics covered in this book are very important in Electrical Engineering, especially Signal Processing, and Applied Mathematics.