About this book
This textbook provides a rigorous mathematical perspective on error-correcting codes, starting with the basics and progressing through to the state-of-the-art. Algebraic, combinatorial, and geometric approaches to coding theory are adopted with the aim of highlighting how coding can have an important real-world impact. Because it carefully balances both theory and applications, this book will be an indispensable resource for readers seeking a timely treatment of error-correcting codes.
Early chapters cover fundamental concepts, introducing Shannon’s theorem, asymptotically good codes and linear codes. The book then goes on to cover other types of codes including chapters on cyclic codes, maximum distance separable codes, LDPC codes, p-adic codes, amongst others. Those undertaking independent study will appreciate the helpful exercises with selected solutions.
A Course in Algebraic Error-Correcting Codes suits an interdisciplinary audience at the Masters level, including students of mathematics, engineering, physics, and computer science. Advanced undergraduates will find this a useful resource as well. An understanding of linear algebra is assumed.
- Book Title A Course in Algebraic Error-Correcting Codes
- Series Title Compact Textbooks in Mathematics
- Series Abbreviated Title Compact Textbooks in Mathematics
- DOI https://doi.org/10.1007/978-3-030-41153-4
- Copyright Information Springer Nature Switzerland AG 2020
- Publisher Name Birkhäuser, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Softcover ISBN 978-3-030-41152-7
- eBook ISBN 978-3-030-41153-4
- Series ISSN 2296-4568
- Series E-ISSN 2296-455X
- Edition Number 1
- Number of Pages XIII, 177
- Number of Illustrations 7 b/w illustrations, 5 illustrations in colour
Information and Communication, Circuits
Coding and Information Theory
Commutative Rings and Algebras
- Buy this book on publisher's site
“The style is clear and the topics are well presented, which makes the understanding of the subject approachable even for students coming from applied sciences. This is a remarkable textbook for a self-contained introduction to the theory of error-correcting codes and some of their modern topics.” (Matteo Bonini, zbMATH 1454.94142, 2021)