| Coding Theory and Number Theory 2003 Edition Contributor(s): Hiramatsu, T. (Author), Köhler, Günter (Author) |
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ISBN: 1402012039 ISBN-13: 9781402012037 Publisher: Springer OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: April 2003 Annotation: This introductory book, which grew out of lectures given at the Mathematics Institute of W??rzburg University, proposes a combination of coding theory and number theory. Chapter 1 gives a standard course of linear codes. The next two chapters treat a link between coding theory and number theory. Chapter 4 is a systematic study of algebraic-geometric codes and in Chapter 5 a connection between binary linear codes and theta functions is discussed. The book is designed to teach undergraduates and graduates the basic ideas and techniques of coding theory and number theory. |
| Additional Information |
| BISAC Categories: - Computers | Information Theory - Mathematics | Discrete Mathematics - Mathematics | Geometry - Algebraic |
| Dewey: 003.54 |
| LCCN: 2003044749 |
| Series: Mathematics and Its Applications |
| Physical Information: 0.5" H x 7" W x 9.18" (0.95 lbs) 148 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: This book grew out of our lectures given in the Oberseminar on 'Cod- ing Theory and Number Theory' at the Mathematics Institute of the Wiirzburg University in the Summer Semester, 2001. The coding the- ory combines mathematical elegance and some engineering problems to an unusual degree. The major advantage of studying coding theory is the beauty of this particular combination of mathematics and engineering. In this book we wish to introduce some practical problems to the math- ematician and to address these as an essential part of the development of modern number theory. The book consists of five chapters and an appendix. Chapter 1 may mostly be dropped from an introductory course of linear codes. In Chap- ter 2 we discuss some relations between the number of solutions of a diagonal equation over finite fields and the weight distribution of cyclic codes. Chapter 3 begins by reviewing some basic facts from elliptic curves over finite fields and modular forms, and shows that the weight distribution of the Melas codes is represented by means of the trace of the Hecke operators acting on the space of cusp forms. Chapter 4 is a systematic study of the algebraic-geometric codes. For a long time, the study of algebraic curves over finite fields was the province of pure mathematicians. In the period 1977 - 1982, V. D. Goppa discovered an amazing connection between the theory of algebraic curves over fi- nite fields and the theory of q-ary codes. |