“Error correcting codes constitute one of the key ingredients in achieving the high degree of reliability required in modern data transmission and storage systems.” With this sentence, Ron Roth sets the stage for his textbook on coding systems. The book is based on the author’s notes from an introductory course on coding theory taught in the computer science department at Technion, Israel Institute of Technology.

The book contains 14 chapters ranging from the basic introduction of terms and a general definition of the coding theory problem to more advanced topics, such as codes developed around mathematical structures (for example, directed graphs and linear finite state machines). The two chapters on the underlying mathematics--“Introduction to Finite Fields” and “Structure of Finite Fields”--were especially easy to follow. Each chapter includes an extensive set of problems followed by notes. The problems help crystallize the concepts taught in the chapter. Some have hints, but there are no solutions. The notes provide interesting extensions of the material covered in the chapters.

The book is written in an algebraic style--notation and abbreviations are introduced once and used extensively afterward. More than once, I found myself looking back to the place where a term was introduced in order to understand what was being said. Perhaps when this material is presented in a course, instructors will provide some redundancy in their lectures, reminding students what a term means as it is being used. There are over 400 references in the bibliography, as well as an excellent index.