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.


  • 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|282 pages

Coding Fundamentals

chapter 1|42 pages

Basics of Coding Theory

ByW. Cary Huffman, Jon-Lark Kim, Patrick Solé

chapter 2|16 pages

Cyclic Codes over Finite Fields

ByCunsheng Ding

chapter 3|18 pages

Construction and Classification of Codes

ByPatric R. J. Östergård

chapter 4|18 pages

Self-Dual Codes

ByStefka Bouyuklieva

chapter 5|14 pages

Codes and Designs

ByVladimir D. Tonchev

chapter 6|18 pages

Codes over Rings

BySteven T. Dougherty

chapter 7|22 pages

Quasi-Cyclic Codes

ByCem Güneri, San Ling, Buket Özkaya

chapter 8|30 pages

Introduction to Skew-Polynomial Rings and Skew-Cyclic Codes

ByHeide Gluesing-Luerssen

chapter 9|16 pages

Additive Cyclic Codes

ByJürgen Bierbrauer, Stefano Marcugini, Fernanda Pambianco

chapter 10|30 pages

Convolutional Codes

ByJulia Lieb, Raquel Pinto, Joachim Rosenthal

chapter 11|24 pages

Rank-Metric Codes

ByElisa Gorla

chapter 12|16 pages

Linear Programming Bounds

ByPeter Boyvalenkov, Danyo Danev

part II|270 pages

Families of Codes

chapter 14|22 pages

Coding Theory and Galois Geometries

ByLeo Storme

chapter 15|56 pages

Algebraic Geometry Codes and Some Applications

ByAlain Couvreur, Hugues Randriambololona

chapter 16|22 pages

Codes in Group Algebras

ByWolfgang Willems

chapter 17|44 pages

Constacyclic Codes over Finite Commutative Chain Rings

ByHai Q. Dinh, Sergio R. López-Permouth

chapter 19|14 pages

Two-Weight Codes

ByAndries E. Brouwer

chapter 20|64 pages

Linear Codes from Functions

BySihem Mesnager

chapter 21|26 pages

Codes over Graphs

ByChristine A. Kelley

part III|270 pages


chapter 22|20 pages

Alternative Metrics

ByMarcelo Firer

chapter 23|24 pages

Algorithmic Methods

ByAlfred Wassermann

chapter 24|14 pages

Interpolation Decoding

BySwastik Kopparty

chapter 25|32 pages

Pseudo-Noise Sequences

ByTor Helleseth, Chunlei Li

chapter 26|12 pages

Lattice Coding

ByFrédérique Oggier

chapter 27|16 pages

Quantum Error-Control Codes

ByMartianus Frederic Ezerman

chapter 28|12 pages

Space-Time Coding

ByFrédérique Oggier

chapter 29|30 pages

Network Codes

ByFrank R. Kschischang

chapter 30|20 pages

Coding for Erasures and Fountain Codes

ByIan F. Blake

chapter 31|28 pages

Codes for Distributed Storage

ByVinayak Ramkumar, Myna Vajha, S. B. Balaji, M. Nikhil Krishnan, Birenjith Sasidharan, P. Vijay Kumar

chapter 32|22 pages

Polar Codes

ByNoam Presman, Simon Litsyn

chapter 33|14 pages

Secret Sharing with Linear Codes

ByCunsheng Ding

chapter 34|24 pages

Code-Based Cryptography

ByPhilippe Gaborit, Jean-Christophe Deneuville