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Continued from the back cover: "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 description 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."
Part I: An elementary introduction to coding
The concept of coding
Binary linear codes
General linear codes
Singleton bound and Reed-Solomon codes
Recursive constructions I
Universal hashing
Designs and the binary Golay code
Shannon entropy
Asymptotic results
3-dimensional codes, projective planes
Summary and outlook
Part II: Theory and applications of codes
Subfield codes and trace codes
Cyclic codes
Recursive constructions, covering radius
OA in statistics and computer science
The geometric descriptions of codes
Additive codes
The last chapter
A References section concludes the book.
This book belongs in the "Discrete Mathematics and Its Applications" series edited by Kenneth H. Rosen, Ph.D.
