Algebraic Codes on Lines, Planes, and Curves: An Engineering Approach

ISBN-13: 9780521771948 / Angielski / Twarda / 2008 / 576 str.

Richard Blahut

Opis

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.

Recenzje

"... a rich, detailed, but fundamentally elementary take on material previously available only to specialists... will be valuable for academic libraries."
D.V. Feldman, University of New Hampshire for Choice Magazine

Spis treści

1. Sequences and the one-dimensional Fourier transform; 2. The Fourier transform and cyclic codes; 3. The many decoding algorithms for Reed-Solomon codes; 4. Within or beyond the packing radius; 5. Arrays and the two-dimensional Fourier transform; 6. The Fourier transform and bicyclic codes; 7. Arrays and the algebra of bivariate polynomials; 8. Computation of minimal bases; 9. Curves, surfaces, and vector spaces; 10. Codes on curves and surfaces; 11. Other representations of codes on curves; 12. The many decoding algorithms for codes on curves.