Poset Codes: Partial Orders, Metrics and Coding Theory

Beschreibung

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.




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.


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

Autor*in

Marcelo Firer

Themen in »Poset Codes: Partial Orders, Metrics and Coding Theory«

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

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“The book’s contents are well chosen and well structured, and the book is accessible and easy to read. … this is an excellent exposition on poset codes and will undoubtedly be used both as a work of reference for researchers and as a course book for undergraduate students.” (Thomas Britz, Mathematical Reviews, July, 2019)
“For a mathematically mature audience, this advanced monograph compiles and presents poset metrics in a systematic way. Instead of reading many papers, one can study the area all in one place. The book can be useful to mathematically oriented electrical engineering and computer science researchers.” (M. M. Tanik, Computing Reviews, October 17, 2019)

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