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＜電子ブック＞
Poset Codes: Partial Orders, Metrics and Coding Theory / by Marcelo Firer, Marcelo Muniz S. Alves, Jerry Anderson Pinheiro, Luciano Panek
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2018.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2018
大きさ	IX, 127 p. 6 illus : online resource
著者標目	*Firer, Marcelo author S. Alves, Marcelo Muniz author Pinheiro, Jerry Anderson author Panek, Luciano author SpringerLink (Online service)
件　名	LCSH:Algebra LCSH:Coding theory LCSH:Information theory LCSH:Convex geometry  LCSH:Discrete geometry LCSH:Number theory FREE:Order, Lattices, Ordered Algebraic Structures FREE:Coding and Information Theory FREE:Convex and Discrete Geometry FREE:Number Theory
一般注記	Chapter 01- Introduction -- Chapter 02- Basic concepts of coding theory -- Chapter 03- Poset metrics -- Chapter 04- Hierarquical posets -- Chapter 05- Disjoint chains with equal length -- Chapter 06- The general case: Coding invariants -- Chapter 07- Duality -- Chapter 08- Generalizations 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 HTTP:URL=https://doi.org/10.1007/978-3-319-93821-9

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