Mathematics in Coding Theory

Author: Garrett
Publisher:
Publish Date: 2005-01-01
Features: This book first introduces the main and fundamental results of communication theory from the perspectives of information theory and probability theory: Shannon's coding theory. Then, it dedicates most of its content to explaining important methods for constructing error-correcting codes. Before each method, it discusses the necessary number theory and modern algebra tools. The final chapter also introduces algebraic geometry codes in a popular and accessible manner, covering advanced content. The book has the following main features: First, it systematically introduces the mathematical foundations, particularly finite fields and number theory, in coding theory. There are few textbooks in China that specifically focus on the mathematical foundations of coding, making this book a significant contribution in filling this gap. The book introduces all the mathematical knowledge used in coding, making it self-contained and well-coordinated in terms of knowledge flow. Second, for the content of coding, the book not only systematically elaborates on the principles of coding theory but also covers the fundamental knowledge of information theory, such as information quantity, entropy, and channel capacity. Another major feature of the book is its gradual and progressive approach, starting from basic concepts and moving toward more advanced topics. Additionally, the book is accompanied by numerous examples and exercises, with content arranged in a way suitable for both teaching and self-study. The author is a renowned number theory professor at the University of Minnesota in the United States. After reading this textbook, readers not only master the mathematical knowledge but also gain insights into its broad application prospects, while also acquiring coding knowledge. This book is suitable as a textbook for algebraic coding theory courses in mathematics departments and departments of information and computational science.