Algebraic Coding Theory Over Finite Commutative Rings (original) (raw)
Overview
Authors:
- Steven T. Dougherty
- Department of Mathematics, University of Scranton , Scranton, USA
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
Includes supplementary material: sn.pub/extras
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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.
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Table of contents (6 chapters)
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)
Authors and Affiliations
Department of Mathematics, University of Scranton , Scranton, USA
Steven T. Dougherty
About the author
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.
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Bibliographic Information
- Book Title: Algebraic Coding Theory Over Finite Commutative Rings
- Authors: Steven T. Dougherty
- Series Title: SpringerBriefs in Mathematics
- DOI: https://doi.org/10.1007/978-3-319-59806-2
- Publisher: Springer Cham
- eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
- Copyright Information: The Author(s) 2017
- Softcover ISBN: 978-3-319-59805-5Published: 14 July 2017
- eBook ISBN: 978-3-319-59806-2Published: 04 July 2017
- Series ISSN: 2191-8198
- Series E-ISSN: 2191-8201
- Edition Number: 1
- Number of Pages: X, 103
- Topics: Associative Rings and Algebras, Information and Communication, Circuits