Algebraic Codes on Lines, Planes, and Curves
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Algebraic geometry is often employed to encode and decode signals transmitted in communication systems. This book describes the fundamental principles of algebraic coding theory from the perspective of an engineer, discussing a number of applications in communications and signal processing. The principal concept is that of using algebraic curves over finite fields to construct error-correcting codes. The most recent developments are presented including the theory of codes on curves, without the use of detailed mathematics, substituting the intense theory of algebraic geometry with Fourier transform where possible. The author describes the codes and corresponding decoding algorithms in a manner that allows the reader to evaluate these codes against practical applications, or to help with the design of encoders and decoders. This book is relevant to practicing communication engineers and those involved in the design of new communication systems, as well as graduate students and researchers in electrical engineering.