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
General
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