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Poset codes : partial orders, metrics and coding theory
Firer M., Alves M., Pinheiro J., Panek L., Springer International Publishing, New York, NY, 2018. 140 pp. Type: Book (978-3-319938-20-2)
Date Reviewed: Oct 17 2019

The authors of this book, part of the “SpringerBriefs in Mathematics” series, have extensive backgrounds in the area covered.

The book, organized into seven chapters, starts with a comprehensive preface, which includes historical background such as Brualdi et al.’s “concept of a metric on a vector space determined by a partial order over a finite set, a poset.” The preface claims that this book is “the first title to give a systematic approach [to] poset metrics and code.” As a skeptic, I wanted to check this claim, so over a two-week period I searched for the contrary; I am now convinced that this book is the first comprehensive coverage of the area. It should be the starting point for anyone interested in poset metrics and codes. However, a word of caution: a reasonable knowledge of coding theory, vector spaces, some combinatorics, and general mathematics is needed to get the most out of this work. The book reads like something in between a research monograph and an advanced text on the topic of poset metrics and codes. As a practitioner of coding theory in engineering, I found the book useful for general awareness but not for practical use.

Each chapter starts with a nice introduction and ends with concluding remarks as “Chapter Notes.” These notes are useful for readers who want a general idea without digging into the details covered in the chapter. Although the preface states that there is an epilogue after chapter 7, I could not find one.

In conclusion, 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.

Reviewer:  M. M. Tanik Review #: CR146736 (2002-0015)
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General (G.0 )
 
 
Hierarchical Design (D.4.7 ... )
 
 
Metrics (D.2.8 )
 
 
Coding And Information Theory (E.4 )
 
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