CODING THEORY a first course

Abstract

As the title of this book already suggests, this manuscript is intended to be a textbook suitable for a first course in coding theory. It is based on a course that is taught for several years at the Eindhoven University of Technology. The students that follow this course are mostly in the third or fourth year of their undergraduate program. Typically, half of them are computer science students, a third of them study mathematics and the remainder are students in electrical engineering or information technology. All these students are familiar with linear algebra and have at least a rudimentary knowledge of probability theory. More importantly, it is assumed here that they are familiar with the theory of finite fields and with elementary number theory. Clearly the latter is not the case at many universities. It is for this reason that a large appendix has been added (Appendix A), containing all the necessary prerequisites with regard to finite field theory and elementary number theory. All chapters contain exercises that we urge the students to solve. Working at these problems seems to be the only way to master this field. As a service to the student that is stranded with a problem or to give a student a chance to look at a (possibly different) solution, all problems are completely worked out in Appendix C. The main part of this manuscript was written at the University of Pretoria in the summer of 1991.