This original monograph investigates several unsolved problems that currentlyexist in coding theory. A highly relevant branch of mathematical computer science, the theory of error-correcting codes is concerned with reliably transmitting data over a ‘noisy’ channel. Despite its fairly long history and consistent prominence, the field still contains interesting problems that have resisted solution by some of the most prominent mathematicians of recent decades. Employing SAGE—a free open-source mathematics software system—to illustrate ideas, this book is intended for graduate students and researchers in algebraic coding theory, especially those who are interested in finding some current unsolved problems. Familiarity with concepts in algebra, number theory, and modular forms is assumed. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study. SAGE, a free open-source mathematics software system, is used with concrete examples in order to emphasize the computational aspects of coding theory. Introduces and explores unsolved open problems in an effort to illuminate the fundamentals of coding theory and stimulate further research. Appeals to academia and industry with real-world applications in electrical engineering and digital communication. INDICE: Preface. Background. Codes and Lattices. Kittens and Blackjack. RHand Coding Theory. Hyperelliptic Curves and QR Codes. Codes from Modular Curves. Appendix. Bibliography. Index.
- ISBN: 978-0-8176-8255-2
- Editorial: Birkhäuser Boston
- Encuadernacion: Cartoné
- Páginas: 248
- Fecha Publicación: 28/10/2011
- Nº Volúmenes: 1
- Idioma: Inglés