Concise Encyclopedia of Coding Theory

<p>Most coding theory experts date the origin of the subject with the 1948 publication of <i>A Mathematical Theory of Communication</i> 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.</p><p>Most topics covered in<i> </i>the <i>Concise Encyclopedia of Coding Theory </i>are presented in short sections at an introductory level and progress from basic to advanced level with definitions examples and many references.</p><p>The book is divided into three parts: </p><p>Part I fundamentals: cyclic codes skew cyclic codes quasi-cyclic codes self-dual codes codes and designs codes over rings convolutional codes performance bounds</p><p>Part II families: AG codes group algebra codes few-weight codes Boolean function codes codes over graphs</p><p>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.</p><p>Features</p><ul> <p> </p> <li>Suitable for students and researchers in a wide range of mathematical disciplines</li> <p> </p> <li>Contains many examples and references</li> <p> </p> <li>Most topics take the reader to the frontiers of research</li> </ul>