A Course in Algebraic Error-Correcting Codes

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 atthe 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.

Provides a rigorous mathematical perspective on error-correcting codes Offers a pathway from the basics to the state-of-the-art, suitable for either independent study or the classroom Corresponds to a one-semester course, where each chapter suits a two-hour lecture Includes numerous helpful exercises with selected solutions provided Includes supplementary material: sn.pub/extras

Autorentext

Simeon Ball is senior lecturer at the Department of Mathematics of the Universitat Politècnica de Catalunya in Barcelona. He has been invited speaker at many international conferences, as well as serving on the scientific and organising committee for many conferences. His research interests include classical and quantum error-correcting codes, incidence problems in real and finite geometries, graphs and semifields, and is particularly focused on applying geometrical and algebraic methods to these combinatorial objects. He has published more than 70 research papers and two books and serves on the editorial board of the Journal of Geometry and the Journal of Combinatorial Theory Series A, having previously served on the editorial board of Designs, Codes and Cryptography and Finite Fields and Their Applications. Oriol Serra is full professor at the Department of Mathematics of the Universitat Politècnica de Catalunya in Barcelona. His research interestsare in combinatorics, graph theory and combinatorial number theory. He has been particularly interested in isoperimetric problems, Ramsey Theory, extremal and probabilistic combinatorics and additive combinatorics. He has published more than 100 research and divulgation papers, has been invited speaker in key conferences and has been involved in the organization of several of them. He has been involved in teaching Combinatorics and Graph Theory at undergraduate and master levels, particularly in a successful course on the topic jointly with Prof. Simeon Ball. He has served as chair of the department of mathematics, vicedean of research of the School of Mathematics at UPC and member of the Executive Committee of the Barcelona Graduate School of Mathematics among other duties.

Inhalt
Euclidean Plane.- Sphere.- Stereographic Projection and Inversions.- Hyperbolic Plane.- Lorentz-Minkowski Plane.- Geometry of Special Relativity.- Answers to Selected Exercises.- Index.