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Poset Codes: Partial Orders, Metrics and Coding Theory

By: Marcelo Firer,Marcelo Muniz S. Alves,Jerry Anderson Pinheiro,Luciano Panek

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Poset Codes: Partial Orders, Metrics and Coding Theory

By: Marcelo Firer,Marcelo Muniz S. Alves,Jerry Anderson Pinheiro,Luciano Panek

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, were 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 coding theory for poset metrics and generalizations. Each chapter includes a survey of the topic presented and a list of exercises, drawn in part from recently proven results. 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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Page Count

133

Publisher

Springer

Published Date

ISBN 10

3319938215

ISBN 13

9783319938219

Poset Codes: Partial Orders, Metrics and Coding Theory

By: Marcelo Firer,Marcelo Muniz S. Alves,Jerry Anderson Pinheiro,Luciano Panek

Write a review Read reviews Take a Quiz Solve Book Puzzle

Poset Codes: Partial Orders, Metrics and Coding Theory

By: Marcelo Firer,Marcelo Muniz S. Alves,Jerry Anderson Pinheiro,Luciano Panek

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, were 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 coding theory for poset metrics and generalizations. Each chapter includes a survey of the topic presented and a list of exercises, drawn in part from recently proven results. 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.

Average ratings

N/A

5

0%

4

0%

3

0%

2

0%

1

0%

Solve jigsaw puzzle

Age

Page Count

133

Publisher

Springer

Published Date

ISBN 10

3319938215

ISBN 13

9783319938219