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Concise Encyclopedia of Coding Theory

Edited by: W. Cary Huffman , Jon-Lark Kim , Patrick Solé

Print publication date:  March  2021
Online publication date:  March  2021

Print ISBN: 9781138551992
eBook ISBN: 9781315147901
Adobe ISBN:

 Cite  Marc Record

Book description

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

Table of contents

Prelims Download PDF
Chapter  1:  Basics of Coding Theory Download PDF
Chapter  2:  Cyclic Codes over Finite Fields Download PDF
Chapter  3:  Construction and Classification of Codes Download PDF
Chapter  4:  Self-Dual Codes Download PDF
Chapter  5:  Codes and Designs Download PDF
Chapter  6:  Codes over Rings Download PDF
Chapter  7:  Quasi-Cyclic Codes Download PDF
Chapter  8:  Introduction to Skew-Polynomial Rings and Skew-Cyclic Codes Download PDF
Chapter  9:  Additive Cyclic Codes Download PDF
Chapter  10:  Convolutional Codes Download PDF
Chapter  11:  Rank-Metric Codes Download PDF
Chapter  12:  Linear Programming Bounds Download PDF
Chapter  13:  Semidefinite Programming Bounds for Error-Correcting Codes Download PDF
Chapter  14:  Coding Theory and Galois Geometries Download PDF
Chapter  15:  Algebraic Geometry Codes and Some Applications Download PDF
Chapter  16:  Codes in Group Algebras Download PDF
Chapter  17:  Constacyclic Codes over Finite Commutative Chain Rings Download PDF
Chapter  18:  Weight Distribution of Trace Codes over Finite Rings Download PDF
Chapter  19:  Two-Weight Codes Download PDF
Chapter  20:  Linear Codes from Functions Download PDF
Chapter  21:  Codes over Graphs Download PDF
Chapter  22:  Alternative Metrics Download PDF
Chapter  23:  Algorithmic Methods Download PDF
Chapter  24:  Interpolation Decoding Download PDF
Chapter  25:  Pseudo-Noise Sequences Download PDF
Chapter  26:  Lattice Coding Download PDF
Chapter  27:  Quantum Error-Control Codes Download PDF
Chapter  28:  Space-Time Coding Download PDF
Chapter  29:  Network Codes Download PDF
Chapter  30:  Coding for Erasures and Fountain Codes Download PDF
Chapter  31:  Codes for Distributed Storage Download PDF
Chapter  32:  Polar Codes Download PDF
Chapter  33:  Secret Sharing with Linear Codes Download PDF
Chapter  34:  Code-Based Cryptography Download PDF
Bibliography Download PDF
Index Download PDF
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