A Course in Algebraic Error-Correcting Codes
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Beschreibung
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.
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
Autor*in
Simeon Ball
Themen in »A Course in Algebraic Error-Correcting Codes«
Coding theory Coding theory error correction Error-correcting codes Algebraic error-correcting codes Shannon's theorem Shannon-Hartley theorem Finite fields Block codes Linear codes Linear code coding theory Cyclic code Cyclic code error detection MDS codes Algebraic geometric codes p-adic codes
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“Merit of this book is its ability to bring together many topics, including current research, in a compact volume. Moreover, throughout the book, the author provides exercises that stimulate the interest of the reader. 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)
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