Algebraic Methods for Signal Processing and Communications Coding

This work aims to explore the links between digital signal processing and error-control codes, with the ultimate intention of 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 can be unified. Because there are many fields and many Fourier transforms in most of these fields, the unified view also reveals a diverse set of mathematical tools, many of which yet to find an appropriate engineering application.