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 . Language: English