Algebraic Coding Theory Over Finite Commutative Rings

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.

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

Auteur
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.

Contenu
Introduction.- Ring Theory.- MacWilliams Relations.- Families of Rings.- Self-Dual Codes.- Cyclic and Constacyclic Codes.