SpringerBriefs in Mathematics

Algebraic Coding Theory Over Finite Commutative Rings

Authors: Dougherty, Steven T.

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  • Presents the foundations required to study codes over rings 
  • Offers generalizations of the classical bounds of coding theory
  • Gives a complete proof of the generalized MacWilliams relations for codes over rings
  • Includes numerous examples to illustrate abstract notions
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eBook $54.99
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  • ISBN 978-3-319-59806-2
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Softcover $69.99
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  • ISBN 978-3-319-59805-5
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About this book

This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account on the subject.

Coding theory has its origins in the engineering problem of effective electronic communication where the alphabet is generally the binary field. Since its inception, it has grown as a branch of mathematics, and has since been expanded to consider any finite field, and later also Frobenius rings, as its alphabet. This book presents a broad view of the subject as a branch of pure mathematics and relates major results to other fields, including combinatorics, number theory and ring theory.

Suitable for graduate students, the book will be of interest to anyone working in the field of coding theory, as well as algebraists and number theorists looking to apply coding theory to their own work.


About the authors

Steven T. Dougherty is professor of mathematics and the 2005 recipient of the Hasse Prize. He has authored numerous publications in coding theory, algebra, combinatorics, number theory and game theory. He has lectured extensively in eleven different countries.

Reviews

“This book offers a comprehensive and thorough presentation of crucial research of the field of algebraic coding theory over finite commutative rings, particularly over finite Frobenius rings. It is also a good guide to the literature on the subject. ... This book will be of interest to graduate students and to anyone working in the field of algebraic coding theory, and its applications.” (Piroska Lakatos, zbMATH 1375.94002, 2018)


Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-319-59806-2
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-59805-5
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Coding Theory Over Finite Commutative Rings
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-59806-2
DOI
10.1007/978-3-319-59806-2
Softcover ISBN
978-3-319-59805-5
Series ISSN
2191-8198
Edition Number
1
Number of Pages
X, 103
Topics