Algebraic codes on lines, planes, and curves: an engineering approach

Algebraic geometry is often employed to encode and decode signals transmittedin 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 principle concept is that of using algebraic curves over finite fields to construct error-correcting codes. The most recent developments are presented including the theoryof codes on curves, without the use of detailed mathematics, substituting theintense 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 practising communication engineers and those involved in the design of new communication systems, as well as graduate students and researchers in electrical engineering. INDICE: 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 forcodes on curves

• ISBN: 978-0-521-77194-8
• Editorial: Cambridge University
• Encuadernacion: Cartoné
• Páginas: 576
• Fecha Publicación: 01/04/2008
• Nº Volúmenes: 1
• Idioma: Inglés