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Algebraic Coding Theory Over Finite Commutative Rings

  • Book
  • © 2017

Overview

Authors:
  1. Steven T. Dougherty

    1. Department of Mathematics, University of Scranton , Scranton, USA

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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
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
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  2. Introduction

    • Steven T. Dougherty
    Pages 1-11

  3. Ring Theory

    • Steven T. Dougherty
    Pages 13-28

  4. MacWilliams Relations

    • Steven T. Dougherty
    Pages 29-40

  5. Families of Rings

    • Steven T. Dougherty
    Pages 41-58

  6. Self-dual Codes

    • Steven T. Dougherty
    Pages 59-81

  7. Cyclic and Constacyclic Codes

    • Steven T. Dougherty
    Pages 83-100

  8. Back Matter

    Pages 101-103
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Keywords

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.



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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