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SpringerBriefs in Mathematics

Poset Codes: Partial Orders, Metrics and Coding Theory

Authors: Firer, M., S. Alves, M.M., Pinheiro, J.A., Panek, L.

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  • Presents poset metrics in a clearly structured and systematic way, gathering together results so far only available in a scattered range of papers
  • Includes a survey on additional, new generalizations for metrics determined by posets
  • Addresses the needs of graduate students and researchers in Mathematics, Electrical Engineering and Computer Sciences
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eBook 44,02 €
price for Spain (gross)
  • ISBN 978-3-319-93821-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-3-319-93820-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this book

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.

About the authors

Marcelo Firer holds Bachelor’s (1989) and Master’s (1991) degrees in Mathematics from the University of Campinas (Unicamp), Brazil, and received his PhD in Mathematics from the Hebrew University of Jerusalem (1997), Israel, under the supervision of Dr. Ilya Rips. He is currently a researcher at the Department of Mathematics at Unicamp, where he has worked since 1999. During this period his research focus has shifted from differential geometry and symmetric spaces to discrete geometrical problems in the context of Coding Theory.

Marcelo Muniz S. Alves completed his Bachelor’s (1996), Master’s (1998) and PhD (2002) studies in Mathematics at the University of Campinas (Unicamp), Brazil. In 2002 he joined the Department of Mathematics at the Federal University of Paraná (UFPR), Brazil, where he works as an Associate Professor. His current research is focused on poset codes and, in particular, codes in the Rosenbloom-Tsfasman metric. In addition, he is pursuing research on actions and representations of Hopf algebras.

Jerry Anderson Pinheiro holds a Master’s degree (2011) and a PhD (2016), both in Mathematics, from the University of Campinas (Unicamp), Brazil, (2016), with studies at the University College Dublin, Claude Shannon Institute, Ireland (2013). His research interests lie in combinatorics, coding theory, discrete geometry and information theory.

Luciano Panek is a professor at the State University of West Paraná, Brazil. He received his Bachelor’s and PhD degrees from the State University of Maringá, Brazil, in 2000 and 2012, respectively, both in Mathematics, and his Master’s degree in Mathematics (2003) from the University of Campinas, Brazil. His research fields include error-correcting codes, information theory and discrete mathematics.


Table of contents (7 chapters)

Table of contents (7 chapters)

Buy this book

eBook 44,02 €
price for Spain (gross)
  • ISBN 978-3-319-93821-9
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 57,19 €
price for Spain (gross)
  • ISBN 978-3-319-93820-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Poset Codes: Partial Orders, Metrics and Coding Theory
Authors
Series Title
SpringerBriefs in Mathematics
Copyright
2018
Publisher
Springer International Publishing
Copyright Holder
The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature
eBook ISBN
978-3-319-93821-9
DOI
10.1007/978-3-319-93821-9
Softcover ISBN
978-3-319-93820-2
Series ISSN
2191-8198
Edition Number
1
Number of Pages
IX, 127
Number of Illustrations
6 b/w illustrations
Topics