Advertisement

Poset Codes: Partial Orders, Metrics and Coding Theory

  • Marcelo Firer
  • Marcelo Muniz S. Alves
  • Jerry Anderson Pinheiro
  • Luciano Panek

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Marcelo Firer, Marcelo Muniz S. Alves, Jerry Anderson Pinheiro, Luciano Panek
    Pages 1-18
  3. Marcelo Firer, Marcelo Muniz S. Alves, Jerry Anderson Pinheiro, Luciano Panek
    Pages 19-38
  4. Marcelo Firer, Marcelo Muniz S. Alves, Jerry Anderson Pinheiro, Luciano Panek
    Pages 39-53
  5. Marcelo Firer, Marcelo Muniz S. Alves, Jerry Anderson Pinheiro, Luciano Panek
    Pages 55-73
  6. Marcelo Firer, Marcelo Muniz S. Alves, Jerry Anderson Pinheiro, Luciano Panek
    Pages 75-91
  7. Marcelo Firer, Marcelo Muniz S. Alves, Jerry Anderson Pinheiro, Luciano Panek
    Pages 93-102
  8. Marcelo Firer, Marcelo Muniz S. Alves, Jerry Anderson Pinheiro, Luciano Panek
    Pages 103-118
  9. Back Matter
    Pages 119-127

About this book

Introduction

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.



Keywords

11T71 94A24 52C26 51E99 Coding Theory discrete geometry Hamming metric Rosenbloom-Tsfasman metric

Authors and affiliations

  • Marcelo Firer
    • 1
  • Marcelo Muniz S. Alves
    • 2
  • Jerry Anderson Pinheiro
    • 3
  • Luciano Panek
    • 4
  1. 1.IMECC — Department of MathematicsUniversity of CampinasCampinasBrazil
  2. 2.Polytechnic Center — Department of MathematicsFederal University of ParanáCuritibaBrazil
  3. 3.IMECC — Department of MathematicsUniversity of CampinasCampinasBrazil
  4. 4.Center of Exact Sciences and EngineeringState University of West ParanáFoz do IguaçuBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-93821-9
  • Copyright Information The Author(s), under exclusive licence to Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-93820-2
  • Online ISBN 978-3-319-93821-9
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • Buy this book on publisher's site