Fundamentals of Error-Correcting Codes

Jul 17, 2026

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Fundamentals of Error-Correcting Codes provides a rigorous introduction to coding theory from both engineering and mathematical perspectives. It covers classical foundations such as linear codes, generator and parity-check matrices, dual codes, weights and distances, and standard constructions for creating new codes. The text extends to modern techniques from specialized literature, including bounds on code size, finite fields, cyclic codes, and major decoding methods for BCH and Reed–Solomon codes, supported by numerous examples and exercises.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages665

Reading Time27 h 56 min

AccessFree to download

Preface

Basic concepts of linear codes

Three fields

Linear codes, generator and parity check matrices

Dual codes

Weights and distances

New codes from old

Permutation equivalent codes

More general equivalence of codes

Hamming codes

The Golay codes

Reed–Muller codes

Encoding, decoding, and Shannon’s Theorem

Sphere Packing Bound, covering radius, and perfect codes

Bounds on the size of codes

Aq(n,d) and Bq(n,d)

The Plotkin Upper Bound

The Johnson Upper Bounds

The Singleton Upper Bound and MDS codes

The Elias Upper Bound

The Linear Programming Upper Bound

The Griesmer Upper Bound

The Gilbert Lower Bound

The Varshamov Lower Bound

Asymptotic bounds

Finite fields

Polynomials and the Euclidean Algorithm

Primitive elements

Constructing finite fields

Cyclic codes

Factoring xn − 1

Basic theory of cyclic codes

Zeros of a cyclic code

Meggitt decoding of cyclic codes

BCH and Reed–Solomon codes

BCH codes

Reed–Solomon codes

Decoding BCH codes

Duadic codes

Fundamentals of Error-Correcting Codes Fundamentals of Error-Correcting Codes is an in-depth introduction to coding theory from both an engineering and mathematical viewpoint. As well as covering classical topics, much coverage is included of recent techniques that until now could only be found in specialist journals and book publications. Numerous exercises and examples and an accessible writing style make this a lucid and effective introduction to coding theory for advanced undergraduate and graduate students, researchers and engineers, whether approaching the subject from a mathematical, engineering, or computer science background. Professor W. Cary Huffman graduated with a PhD in mathematics from the California Institute of Technology in 1974 . He taught at Dartmouth College and Union College until he joined the Department of Mathematics and Statistics at Loyola in 1978, serving as chair of the department from 1986 through 1992 . He is an author of approximately 40 research papers in ﬁnite group theory, combinatorics, and coding theory, which have appeared in journals such as the Journal of Algebra, IEEE Transactions on Information Theory, and the Journal of Combinatorial Theory. Professor Vera Pless was an undergraduate at the University of Chicago and received her PhD from Northwestern in 1957 . After ten years at the Air Force Cambridge Research Laboratory, she spent a few years at MIT’s project MAC. She joined the University of Illinois-Chicago’s Department of Mathematics, Statistics, and Computer Science as a full professor in 1975 and has been there ever since. She is a University of Illinois Scholar and has published over 100 papers. Fundamentals of Error-Correcting Codes W. Cary Huffman Loyola University of Chicago and Vera Pless University of Illinois at Chicago 􀀁􀀂􀀃􀀄􀀅􀀆􀀇􀀈􀀉 􀀋􀀌􀀆􀀍􀀉􀀅􀀎􀀆􀀏􀀐 􀀑􀀅􀀉􀀎􀀎 Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo Cambridge University Press The Edinburgh Building, Cambridge 􀀁􀀄􀀒 􀀒􀀅􀀋, United Kingdom Published in the United States of America by Cambridge University Press, New York [www.cambridge.org](www.cambridge.org) Information on this [title: www.cambridge.org/9780521782807](title: www.cambridge.org/9780521782807) © Cambridge University Press 2003 This book is in copyright. Subject to statutory exception and to the provision of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published in print format 2003 􀀆􀀎􀀄􀀌-􀀔􀀕 􀀖􀀗􀀘-􀀙-􀀚􀀔􀀔-􀀙􀀗􀀗􀀗􀀖-􀀔 eBook (NetLibrary) 􀀆􀀎􀀄􀀌-􀀔􀀙 􀀙-􀀚􀀔􀀔-􀀙􀀗􀀗􀀗􀀖-􀀕 eBook (NetLibrary) 􀀆􀀎􀀄􀀌-􀀔􀀕 􀀖􀀗􀀘-􀀙-􀀚􀀒􀀔-􀀗􀀘􀀒􀀘􀀙-􀀗 hardback 􀀆􀀎􀀄􀀌-􀀔􀀙 􀀙-􀀚􀀒􀀔-􀀗􀀘􀀒􀀘􀀙-􀀚 hardback Cambridge University Press has no responsibility for the persistence or accuracy of 􀀋􀀅􀀛s for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. To Gayle, Kara, and Jonatha

FAQs

What perspectives does the book use to teach coding theory?

The book introduces coding theory from both an engineering viewpoint and a mathematical viewpoint, aiming to serve readers with different backgrounds.

Which foundational topics are covered in the early chapters?

It covers basic linear-code structures such as generator and parity-check matrices, dual codes, weights and distances, and several methods for constructing new codes from existing ones.

What later topics does the book cover beyond linear codes?

Later sections include bounds on code size, finite fields, cyclic codes and their decoding, and BCH and Reed–Solomon codes with multiple decoding algorithms.

Jul 17, 2026

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