Codes, Cryptology and Curves with Computer Algebra

Ruud Pellikaan has tenure at the Technische Universiteit Eindhoven, The Netherlands where his research has shifted from a devotion to coding theory, particularly algebraic geometry codes and their decoding, to code-based cryptography. He previously served as an associate editor of the IEEE Transactions of Information Theory and has organised several conferences. Xin-Wen Wu is a Senior Lecturer at the School of Information and Communication Technology, Griffith University, Queensland. His research interests include coding theory and information theory, cyber and data security, applied cryptography communications and networks. He has published extensively in these areas and is a senior member of Institute of Electrical and Electronics Engineers (IEEE). Stanislav Bulygin works as a technology specialist and product manager in the field of IT security and banking services. He previously worked as a researcher focusing on cryptology and IT security at the Technical University of Darmstadt, Germany. His main research activities were connected to the theory of error-correcting codes and their use in cryptography, quantum resistant cryptosystems and algebraic methods in cryptology. Relinde Jurrius is an Assistant Professor at the Université de Neuchatel, Switzerland. Her research interests are in coding theory, network coding and its connection with other branches of mathematics such as matroid theory, algebraic and finite geometry, and combinatorics. Apart from research and teaching, she is active in organising outreach activities, including a math camp for high school students, a public open day for the Faculty of Science and extra-curricular activities for elementary school children.

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.