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Poset Codes: Partial Orders, Metrics and Coding Theory

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Poset Codes: Partial Orders, Metrics and Coding Theory/ by Marcelo Firer, Marcelo Muniz S. Alves, Jerry Anderson Pinheiro, Luciano Panek.
Author:	Firer, Marcelo.
other author:	S. Alves, Marcelo Muniz.
Description:	IX, 127 p. 6 illus.online resource. :
Contained By:	Springer Nature eBook
Subject:	Algebra. -
Online resource:	https://doi.org/10.1007/978-3-319-93821-9
ISBN:	9783319938219

Poset Codes: Partial Orders, Metrics and Coding Theory
Firer, Marcelo.

Poset Codes: Partial Orders, Metrics and Coding Theory[electronic resource] /by Marcelo Firer, Marcelo Muniz S. Alves, Jerry Anderson Pinheiro, Luciano Panek. - 1st ed. 2018. - IX, 127 p. 6 illus.online resource. - SpringerBriefs in Mathematics,2191-8198. - SpringerBriefs in Mathematics,.

Chapter 01- Introduction -- Chapter 02- Basic concepts of coding theory -- Chapter 03- Poset metrics -- Chapter 04- Hierarquical posets -- Chapter 05- Disjoint chains with equal length -- Chapter 06- The general case: Coding invariants -- Chapter 07- Duality -- Chapter 08- Generalizations.

This book offers an organized and systematic approach to poset metrics and codes. Poset metrics, or metrics on a vector field determined by a partial order over a finite set, was first introduced in the mid-1990s by the mathematicians Richard A. Brualdi, Janine S. Graves and K. Mark Lawrence, and to date the relevant knowledge on this subject was spread over more than two hundred research papers. Poset metrics generalizes both the standard Hamming metric – the most important metric used in the context of coding theory – and the Niederreiter-Rosenbloom-Tsfasman metric, which is an ultrametric. Conceived to be as self-contained as possible, the book starts from basic concepts of coding theory and advances towards poset proprieties and generalizations. Each chapter includes a survey of the topic presented and a list of exercises, drawn in part from recently proven propositions. This work will appeal to researchers and graduate students alike, particularly those in the fields of Mathematics, Electrical Engineering and Computer Sciences, with an interest in discrete geometry and coding theory.

ISBN: 9783319938219

Standard No.: 10.1007/978-3-319-93821-9doiSubjects--Topical Terms:

579870
Algebra.

LC Class. No.: QA172-172.4

Dewey Class. No.: 511.33

Poset Codes: Partial Orders, Metrics and Coding Theory
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520 $a This book offers an organized and systematic approach to poset metrics and codes. Poset metrics, or metrics on a vector field determined by a partial order over a finite set, was first introduced in the mid-1990s by the mathematicians Richard A. Brualdi, Janine S. Graves and K. Mark Lawrence, and to date the relevant knowledge on this subject was spread over more than two hundred research papers. Poset metrics generalizes both the standard Hamming metric – the most important metric used in the context of coding theory – and the Niederreiter-Rosenbloom-Tsfasman metric, which is an ultrametric. Conceived to be as self-contained as possible, the book starts from basic concepts of coding theory and advances towards poset proprieties and generalizations. Each chapter includes a survey of the topic presented and a list of exercises, drawn in part from recently proven propositions. This work will appeal to researchers and graduate students alike, particularly those in the fields of Mathematics, Electrical Engineering and Computer Sciences, with an interest in discrete geometry and coding theory.
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