We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 26 October 2017
An early version of this book was a handwritten manuscript from around 1990. In June 2001 a synopsis was written by invitation of Cambridge University Press with the working title “The construction and decoding of algebraic geometry codes,” or “Algebraic geometry and its applications (in error-correcting codes and cryptography).” That proposal was accepted, but with no indication of a deadline. So originally its aim was a book on algebraic geometry codes. As time passed more and more co-authors joined the team: Xin-Wen Wu in 2004, Stanislav Bulygin in 2007 and finally Relinde Jurrius in 2012.
Early versions of chapters were written on algebraic geometry codes, elementary coding theory, list decoding Reed–Muller codes, decoding algorithms and Gröbner bases, cryptography, weight enumerators and its generalizations and relations with matroid theory that appeared in books and journals [68, 69, 70, 71, 177, 184, 186, 266].
The prerequisites of this book are: elementary logical reasoning and naive set theory, some combinatorics and probability theory. Furthermore: linear algebra, the beginnings of group theory, the algebra of rings and fields. We will go into the details of polynomial rings and finite fields in several chapters.
The first six chapters of the book on the construction, properties and decoding of error-correcting codes are self-contained. This can be used as a course in Coding Theory of four hours a week during a semester in the first year of the Masters. It is advised to use Chapter 12 from the start to practise the theory with computer algebra systems.
The second half of the book on complexity theory, cryptology, Gröbner bases applied to codes and cryptosystems and algebraic geometry codes is more advanced. This can be used for a course in the second year of a Masters degree or can be read individually as a Capita Selecta. It is also a good starting point for a project or assignment. In the Notes at the end of every chapter we give ample references to further reading.
We thank the editors of Cambridge University Press: David Tranah, Jonathan Walthoe, Roger Astley, Clare Dennison and Abigail Walkington for their advice and patience.
To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
Find out more about the Kindle Personal Document Service.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.
To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.
