Overview
- 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
Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)
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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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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