Although its roots lie in information theory, the applications of coding theory now extend to statistics, cryptography, and many areas of pure mathematics, as well as pervading large parts of theoretical computer science, from universal hashing to numerical integration.
Introduction to Coding Theory introduces the theory of error-correcting codes in a thorough but gentle presentation. Part I begins with basic concepts, then builds from binary linear codes and Reed-Solomon codes to universal hashing, asymptotic results, and 3-dimensional codes. Part II emphasizes cyclic codes, applications, and the geometric desciption of codes. The author takes a unique, more natural approach to cyclic codes that is not couched in ring theory but by virtue of its simplicity, leads to far-reaching generalizations. Throughout the book, his discussions are packed with applications that include, but reach well beyond, data transmission, with each one introduced as soon as the codes are developed.
Although designed as an undergraduate text with myriad exercises, lists of key topics, and chapter summaries, Introduction to Coding Theory explores enough advanced topics to hold equal value as a graduate text and professional reference. Mastering the contents of this book brings a complete understanding of the theory of cyclic codes, including their various applications and the Euclidean algorithm decoding of BCH-codes, and carries readers to the level of the most recent research.
Rezensionen / Stimmen
"Although designed as an undergraduate text with myriad exercises, lists of key topics, and chapter summaries, this excellent book explores enough advanced topics to hold equal value as a graduate text and professional reference. Mastering the contents of this book brings a complete understanding of the theory of cyclic codes, including their various applications and the Euclidean algorithm decoding of BCH-codes, and carries readers to the level of the most recent research."
- Cryptologia
"Bierbrauer makes two contributions to ... [the] literature with this book: he presents a method for teaching the basics of theory to undergraduates that includes a discussion of Reed-Solomon codes, and he manages to weave presentations of both the theory and applications of designs ... . The writing is ... readable and in fact enjoyable. ... Those who seek an appropriate undergraduate text in the subject, as well as those who desire a book that incorporates a healthy does of design theory in addition to the basics of coding, may well find this a rewarding text to use in their classrooms."
- Mathematical Reviews, 2005f
"This nice textbook offers a self-contained introduction to mathematical coding theory and its major areas of application."
-Zentralblatt MATH
"I enjoyed reading this book; the author is good about defining terms as he uses them so that the logic can be followed by someone without a background in the area. The sections are short, with relevant problems at the end of each section. ...It should be accessible to the typical computer science gradate student; I would recommend it for a graduate class on coding theory."
-SIGACT News
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Für höhere Schule und Studium
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1000 equations; 19 Illustrations, black and white
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ISBN-13
978-1-4822-9637-2 (9781482296372)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
AN ELEMENTARY INTRODUCTION TO CODING: Preface; The Concept of Coding; Binary Linear Codes; General Linear Codes; Reed-Solomon codes; Recursive Construction I; Universal Hashing; Designs and the Binary Golay Code; Shannon Entropy Asymptotic Results; 3-Dimensional Codes and Projective Planes; THE THEORY OF CODES AND THEIR APPLICATIONS: Summary and Outlook; Subfield Codes and Trace Codes; Cyclic Codes; Recursive Constructions, Covering Radius; Orthogonal Arraysin Statistics and Computer Science; The Geometric Description of Codes; Additive Codes; The last chapter.
