Codes, Cryptology and Curves with Computer Algebra

Graduate-level introduction to error-correcting codes, which are used to protect digital data and applied in public key cryptosystems.

Ruud Pellikaan (Author), Xin-Wen Wu (Author), Stanislav Bulygin (Author), Relinde Jurrius (Author)

9780521817110, Cambridge University Press

Hardback, published 2 November 2017

606 pages, 30 b/w illus. 305 exercises
23.5 x 15.7 x 3.5 cm, 0.98 kg

I was impressed by the scope of the book: many topics in algebraic coding theory are addressed and now collected in one book. Someone reading the entire book, will obtain a very good overview of algebraic coding theory. Peter Beelen, Nieuw Archief voor Weskunde

This well-balanced text touches on theoretical and applied aspects of protecting digital data. The reader is provided with the basic theory and is then shown deeper fascinating detail, including the current state of the art. Readers will soon become familiar with methods of protecting digital data while it is transmitted, as well as while the data is being stored. Both basic and advanced error-correcting codes are introduced together with numerous results on their parameters and properties. The authors explain how to apply these codes to symmetric and public key cryptosystems and secret sharing. Interesting approaches based on polynomial systems solving are applied to cryptography and decoding codes. Computer algebra systems are also used to provide an understanding of how objects introduced in the book are constructed, and how their properties can be examined. This book is designed for Masters-level students studying mathematics, computer science, electrical engineering or physics.

Preface Ruud Pellikaan
1. Error-correcting codes Ruud Pellikaan and Xin-Wen Wu
2. Code constructions and bounds on codes Ruud Pellikaan and Xin-Wen Wu
3. Weight enumeration Relinde Jurrius, Ruud Pellikaan and Xin-Wen Wu
4. Cyclic codes Ruud Pellikaan
5. Polynomial codes Ruud Pellikaan
6. Algebraic decoding Ruud Pellikaan and Xin-Wen Wu
7. Complexity and decoding Stanislav Bulygin, Ruud Pellikaan and Xin-Wen Wu
8. Codes and related structures Relinde Jurrius and Ruud Pellikaan
9. Cryptology Stanislav Bulygin
10. Gröbner bases for coding and cryptology Stanislav Bulygin
11. Codes on curves Ruud Pellikaan
12. Coding and cryptology with computer algebra Stanislav Bulygin
References
Index.

Subject Areas: Maths for computer scientists [UYAM], Maths for engineers [TBJ], Maths for scientists [PDE], Algebra [PBF], Coding theory & cryptology [GPJ], Information theory [GPF]