1st Edition

Concise Encyclopedia of Coding Theory

Edited By W. Cary Huffman, Jon-Lark Kim, Patrick Solé Copyright 2021
    998 Pages 52 B/W Illustrations
    by Chapman & Hall

    998 Pages 52 B/W Illustrations
    by Chapman & Hall

    998 Pages 52 B/W Illustrations
    by Chapman & Hall

    Most coding theory experts date the origin of the subject with the 1948 publication of A Mathematical Theory of Communication by Claude Shannon. Since then, coding theory has grown into a discipline with many practical applications (antennas, networks, memories), requiring various mathematical techniques, from commutative algebra, to semi-definite programming, to algebraic geometry.

    Most topics covered in the Concise Encyclopedia of Coding Theory are presented in short sections at an introductory level and progress from basic to advanced level, with definitions, examples, and many references.

    The book is divided into three parts:

    Part I fundamentals: cyclic codes, skew cyclic codes, quasi-cyclic codes, self-dual codes, codes and designs, codes over rings, convolutional codes, performance bounds

    Part II families: AG codes, group algebra codes, few-weight codes, Boolean function codes, codes over graphs

    Part III applications: alternative metrics, algorithmic techniques, interpolation decoding, pseudo-random sequences, lattices, quantum coding, space-time codes, network coding, distributed storage, secret-sharing, and code-based-cryptography.

    Features

    • Suitable for students and researchers in a wide range of mathematical disciplines
    • Contains many examples and references
    • Most topics take the reader to the frontiers of research

    Part I. Coding Fundamentals

    1. Basics of Coding Theory
    W. Cary Huffman, Jon-Lark Kim, and Patrick Solé

    2. Cyclic Codes over Finite Fields
    Cunsheng Ding

    3. Construction and Classification of Codes.
    Patric R. J. Östergård

    4. Self-Dual Codes
    Stefka Bouyuklieva

    5. Codes and Designs
    Vladimir D. Tonchev

    6. Codes over Rings
    Steven T. Dougherty

    7. Quasi-Cyclic Codes
    Cem Güneri, San Ling, and Buket Özkaya

    8. Introduction to Skew-Polynomial Rings and Skew-Cyclic Codes
    Heide Gluesing-Luerssen

    9. Additive Cyclic Codes
    Jürgen Bierbrauer, Stefano Marcugini, and Fernanda Pambianco

    10. Convolutional Codes
    Julia Lieb, Raquel Pinto, and Joachim Rosenthal

    11. Rank-Metric Codes
    Elisa Gorla

    12. Linear Programming Bounds
    Peter Boyvalenkov and Danyo Danev

    13. Semidefinite Programming Bounds for Error-Correcting Codes
    Frank Vallentin

    Part II. Families of Codes

    14. Coding Theory and Galois Geometries
    Leo Storme

    15. Algebraic Geometry Codes and Some Applications
    Alain Couvreur and Hugues Randriambololona

    16. Codes in Group Algebras
    Wolfgang Willems

    17. Constacyclic Codes over Finite Commutative Chain Rings
    Hai Q. Dinh and Sergio R. López-Permouth

    18. Weight Distribution of Trace Codes over Finite Rings

    Minjia Shi

    19. Two-Weight Codes
    Andries E. Brouwer

    20. Linear Codes from Functions
    Sihem Mesnager

    21. Codes over Graphs
    Christine A. Kelley

    Part III. Applications

    22. Alternative Metrics
    Marcelo Firer

    23. Algorithmic Methods
    Alfred Wassermann

    24. Interpolation Decoding
    Swastik Kopparty

    25. Pseudo-Noise Sequences
    Tor Helleseth and Chunlei Li

    26. Lattice Coding
    Frédérique Oggier

    27. Quantum Error-Control Codes
    Martianus Frederic Ezerman

    28. Space-Time Coding
    Frédérique Oggier

    29. Network Codes
    Frank R. Kschischang

    30. Coding for Erasures and Fountain Codes
    Ian F. Blake

    31. Codes for Distributed Storage
    Vinayak Ramkumar, Myna Vajha, S. B. Balaji, M. Nikhil Krishnan, Birenjith Sasidharan, and P. Vijay Kumar

    32. Polar Codes
    Noam Presman and Simon Litsyn

    33. Secret Sharing with Linear Codes
    Cunsheng Ding

    34. Code-Based Cryptography
    Philippe Gaborit and Jean-Christophe Deneuville

    Bibliography

    Index

    Biography

    W. Cary Huffman (1948-) received his PhD in mathematics from the California Institute of Technology in 1974. He taught at Dartmouth College (1974 – 1976) as a John Wesley Young Research Instructor and then at Union College (1976 – 1978). In 1978, he joined the Department of Mathematics and Statistics at Loyola University Chicago, continuing there until his retirement in 2018; he is now professor emeritus. He served as that department’s chair from 1986 to 1992. He is co-editor of the Handbook of Coding Theory and co-author of Fundamentals of Error-Correcting Codes, both with Vera Pless. In addition, he has published numerous papers in finite group theory, combinatorics, and algebraic coding theory.

    Jon-Lark Kim received his Ph.D. in 2002 from Department of Math of the University of Illinois at Chicago. He was an Associate Professor at the University of Louisville until 2012. He is currently professor at Math Department of Sogang University in Seoul. He has authored more than fifty research papers and one book on Coding Theory. He is the recipient of the 2004 Kirkman medal from the Institute of Combinatorics and its Applications. His research interests include Coding Theory, Cryptography, Combinatorics, Bioinformatics, and Artificial Intelligence.

    Patrick Solé (1960-) received the Ingénieur and the Docteur Ingénieur degrees from Ecole Nationale Supérieure des Télécommunications, Paris, France in 1984 and 1987, respectively, and the Habilitation à Diriger des Recherches degree from University of Nice Sophia-Antipolis, France, in 1993.

    He has held several visiting positions at Syracuse University, Syracuse, NY, in 1987 – 1989, Macquarie University, Sydney, Australia, in 1994 – 1996, and at University des Sciences et Techniques de Lille, Lille, France, in 1999 – 2000. He has been a permanent member of Centre National de la Recherche Scientifique since 1989 and was later promoted to the rank of Senior Researcher (Directeur de Recherche) in 1996.

    His research interests include coding theory (covering radius, codes over rings, geometric codes, quantum codes), interconnection networks (graph spectra, expanders), space time codes (lattices, theta series), and cryptography (Boolean functions, secret sharing schemes).

    He is the author of more than 200 journal papers, and of four books.

    "If you want a comprehensive outline of classical coding theory and its modern applications, you will appreciate this encyclopedia. It is written by a large international group of experts with a wide spread of experience. Extensive references to publications and web sources support the chapters; they allow the reader to follow in depth interests sparked by each topic covered. The vast range of applications detailed makes it evident that coding theory is a major and vital area of mathematics."
    – Emeritus Professor Harold Ward, University of Virginia

    "Featuring a wealth of examples and references, and addressing topics on the cutting edge of research and practice, Concise Encyclopedia of Coding Theory is especially useful for students and researchers in a wide range of mathematical disciplines, as well as is an ideal textbook for coding theory curriculums. While especially and unreservedly recommended for college and university library Combinatorics, Information Theory, and Web Encryption collections and supplemental studies curriculums, it should be noted for the personal reading lists of professional coders, coding students, academia, and non-specialist general readers with an interest in the subject"
    – Midwest Book Review