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Algebraic Coding Theory Over Finite Commutative Rings

  • Steven T.¬†Dougherty

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-x
  2. Steven T. Dougherty
    Pages 1-11
  3. Steven T. Dougherty
    Pages 13-28
  4. Steven T. Dougherty
    Pages 29-40
  5. Steven T. Dougherty
    Pages 41-58
  6. Steven T. Dougherty
    Pages 59-81
  7. Steven T. Dougherty
    Pages 83-100
  8. Back Matter
    Pages 101-103

About this book

Introduction

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.


Keywords

algebraic coding theory frobenius rings MacWilliams relations codes over rings codes over finite rings self-dual codes cyclic codes

Authors and affiliations

  • Steven T.¬†Dougherty
    • 1
  1. 1.Department of MathematicsUniversity of Scranton ScrantonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-59806-2
  • Copyright Information The Author(s) 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-59805-5
  • Online ISBN 978-3-319-59806-2
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site