Finite fields for computer scientists and engineers
Robert J. McEliece
Kluwer Academic Publishers
The theory of finite fields is of central importance in  engineering and computer science, because of its applications to  error-correcting codes, cryptography, spread-spectrum communications,  and digital signal processing. Though not inherently difficult, this  subject is almost never taught in depth in mathematics courses, (and  even when it is the emphasis is rarely on the practical aspect).  Indeed, most students get a brief and superficial survey which is  crammed into a course on error-correcting codes. It is the object of  this text to remedy this situation by presenting a thorough  introduction to the subject which is completely sound mathematically,  yet emphasizes those aspects of the subject which have proved to be  the most important for applications. <br/>  This book is unique in several respects. Throughout, the emphasis is  on fields of characteristic 2, the fields on which almost all  applications are based. The importance of Euclid's algorithm is  stressed early and often. Berlekamp's polynomial factoring algorithm  is given a complete explanation. The book contains the first treatment  of Berlekamp's 1982 bit-serial multiplication circuits, and concludes  with a thorough discussion of the theory of m-sequences, which are  widely used in communications systems of many kinds.