Concise Encyclopedia Of Coding Theory
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Concise Encyclopedia of Coding Theory
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
Essays on Coding Theory
Author: Ian F. Blake
language: en
Publisher: Cambridge University Press
Release Date: 2024-03-14
Critical coding techniques have developed over the past few decades for data storage, retrieval and transmission systems, significantly mitigating costs for governments and corporations that maintain server systems containing large amounts of data. This book surveys the basic ideas of these coding techniques, which tend not to be covered in the graduate curricula, including pointers to further reading. Written in an informal style, it avoids detailed coverage of proofs, making it an ideal refresher or brief introduction for students and researchers in academia and industry who may not have the time to commit to understanding them deeply. Topics covered include fountain codes designed for large file downloads; LDPC and polar codes for error correction; network, rank metric, and subspace codes for the transmission of data through networks; post-quantum computing; and quantum error correction. Readers are assumed to have taken basic courses on algebraic coding and information theory.
CRC Concise Encyclopedia of Mathematics
Upon publication, the first edition of the CRC Concise Encyclopedia of Mathematics received overwhelming accolades for its unparalleled scope, readability, and utility. It soon took its place among the top selling books in the history of Chapman & Hall/CRC, and its popularity continues unabated. Yet also unabated has been the d