Algèbre discrète et codes correcteurs / Odile Papini, Jacques Wolfmann

This book appears as a basic course on error-correcting codes with an algebraic point of view. It results from advanced courses given by the authors in the graduate and post-graduate studies in computer science and mathematics. It is intended for students, researchers and engineers. The first part of the book is devoted to discrete algebra, from elementary algebraic notions to specific algebraic background suitable for coding theory. In particular, all important results about finite fields are presented. The second part of the book deals with the theory of error-correcting codes, giving an overview of the most classical codes. A list of problems is given later, as a complement for the algebraic coding theory. The originality of this book lies in the following additional chapters. First of all, there is an historical part where the error correcting codes are replaced in the knowledge evolution. The links between mathematics and computer science are presented as a context of emergence of this new theory. In the decoding part, different methods are presented, for decoding of linear codes and particularly cyclic codes (as BCH-codes). In each case, the theoretical results which the method stems from and the algorithms are precised. A specific chapter describes some industrial applications of the theory of error correcting codes such as the CIRC code for the Compact Disk, the codes devoted to space data transmission and those used for the Minitel. The research streamlines in the field of error correcting codes, leading to open questions, are presented. Some elementary algebraic results and several tables are given at the end. There is also an extension on algorithms and calculus in finite fields which are suitable for efficient coding and decoding. (Zentralblatt)

Bibliogr. p. [253]-256. Index