02188 2200229 4500
FRBNF374265730000005
3540564896
Berlin
0387564896
New York
6688
6688
19940802d1993 m y0frey5003 b
eng
eng
Algebraic function fields and codes
Henning, Stichtenoth
MON
Berlin
New York
Springer
1993
X-260 p.
24 cm
Universitext
Bibliogr. p. 251-252. Index
This book has two objectives. The first is to fill a void in the existing mathematical literature by providing a modern, self-contained and in-depth exposition of the theory of algebraic function fields. The topics include the Riemann-Roch theorem, algebraic extensions of function fields, ramifications theory and differentials. Particular emphasis is placed on function fields over a finite constant field, leading into zeta functions and the Hasse-Weil theorem. Numerous examples illustrate the general theory. Error-correcting codes are in widespread use for the reliable transmission of information. Perhaps the most fascinating of all the ties that link the theory of these codes to mathematics is the construction by V.D. Goppa, of powerful codes using techniques borrowed from algebraic geometry. Algebraic function fields provide the most elementary approach to Goppa's ideas, and the second objective of this book is to provide an introduction to Goppa's algebraic-geometric codes along these lines. The codes, their parameters and links with traditional codes such as classical Goppa, Peed-Solomon and BCH codes are treated at an early stage of the book. Subsequent chapters include a decoding algorithm for these codes as well as a discussion of their subfield subcodes and trace codes. Stichtenoth's book will be very useful to students and researchers in algebraic geometry and coding theory and to computer scientists and engineers interested in information transmission.
Codage
Fonctions algébriques
Corps algébriques
512.2 Arithmétique, courbes algébriques
Stichtenoth
Henning
13660
6839
ENSB
ENSB
MATHEMATIQUES
00006895
512.2 STI
2013-03-26
0
512.2 Arithmétique, courbes algébriques