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Algebraic coding theory over finite ...

Dougherty, Steven T.

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Algebraic coding theory over finite commutative rings

Record Type:	Electronic resources : Monograph/item
Title/Author:	Algebraic coding theory over finite commutative rings/ by Steven T. Dougherty.
Author:	Dougherty, Steven T.
Published:	Cham :Springer International Publishing : : 2017.,
Description:	x, 103 p. :ill., digital ;24 cm.
[NT 15003449]:	Introduction -- Ring Theory -- MacWilliams Relations -- Families of Rings -- Self-Dual Codes -- Cyclic and Constacyclic Codes.
Contained By:	Springer eBooks
Subject:	Commutative rings. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-59806-2
ISBN:	9783319598062

Algebraic coding theory over finite commutative rings
Dougherty, Steven T.

Algebraic coding theory over finite commutative rings[electronic resource] /by Steven T. Dougherty. - Cham :Springer International Publishing :2017. - x, 103 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

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

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.

ISBN: 9783319598062

Standard No.: 10.1007/978-3-319-59806-2doiSubjects--Topical Terms:

606074
Commutative rings.

LC Class. No.: QA251.3

Dewey Class. No.: 512.44

Algebraic coding theory over finite commutative rings
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020 $a 9783319598062 $q (electronic bk.)
020 $a 9783319598055 $q (paper)
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100 1 $a Dougherty, Steven T. $3 3250914
245 1 0 $a Algebraic coding theory over finite commutative rings $h [electronic resource] / $c by Steven T. Dougherty.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2017.
300 $a x, 103 p. : $b ill., digital ; $c 24 cm.
490 1 $a SpringerBriefs in mathematics, $x 2191-8198
505 0 $a Introduction -- Ring Theory -- MacWilliams Relations -- Families of Rings -- Self-Dual Codes -- Cyclic and Constacyclic Codes.
520 $a 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.
650 0 $a Commutative rings. $3 606074
650 0 $a Coding theory. $3 532585
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Associative Rings and Algebras. $3 897405
650 2 4 $a Information and Communication, Circuits. $3 893882
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer eBooks
830 0 $a SpringerBriefs in mathematics. $3 1566700
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-59806-2
950 $a Mathematics and Statistics (Springer-11649)