The geometry of curves has fascinated mathematicians for 2500 years, and the theory has become highly abstract. Recently links have been made with the subject of error correction, leading to the creation of geometric Goppa codes, a new and important area of coding theory. This book is an updated and extended version of the last part of the successful book Error-Correcting Codes and Finite Fields. It provides an elementary introduction to Goppa codes, and includes many examples, calculations, and applications. The book is in two parts with an emphasis on motivation, and applications of the theory take precedence over proofs of theorems. The formal theory is, however, provided in the second part of the book, and several of the concepts and proofs have been simplified without sacrificing rigour.

Written in 1939 and unpublished until 2000, Sebastian Haffner’s memoir of the rise of Nazism in Germany offers a unique portrait of the lives of ordinary German citizens between the wars. Covering 1907 to 1933, his eyewitness account provides a portrait of a country in constant flux: from the rise of the First Corps, the right-wing voluntary military force set up in 1918 to suppress Communism and precursor to the Nazi storm troopers, to the Hitler Youth movement; from the apocalyptic year of 1923 when inflation crippled the country to Hitler’s rise to power. This fascinating personal history elucidates how the average German grappled with a rapidly changing society, while chronicling day-to-day changes in attitudes, beliefs, politics, and prejudices.

Error correcting codes is an area which has vital importance for the development of signal processing over the next 20 years. The purpose of this book is to provide a theoretical and practical introduction to the subject of error correcting codes. This textbook is a reprint of Chapters 1-20 of the original hardback edition. It provides the reader with the tools necessary to implement modern error-processing schemes, and only a basic knowledge of linear algebra is assumed. More elementary than any of the other books of the same subject, it will be considerably easier for most graduate students to follow. All the necessary mathematics is developed in parallel with the applications. The author has provided a simple step-by-step approach, with worked examples which motivate and explain the theory.