國立虎尾科技大學 |

Poset codes = partial orders, metrics and coding theory /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Poset codes/ by Marcelo Firer ... [et al.].
其他題名:	partial orders, metrics and coding theory /
其他作者:	Firer, Marcelo.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	ix, 127 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Partially ordered sets. -
電子資源:	https://doi.org/10.1007/978-3-319-93821-9
ISBN:	9783319938219

Poset codes = partial orders, metrics and coding theory /
Poset codespartial orders, metrics and coding theory /[electronic resource] :by Marcelo Firer ... [et al.]. - Cham :Springer International Publishing :2018. - ix, 127 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

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.

ISBN: 9783319938219

Standard No.: 10.1007/978-3-319-93821-9doiSubjects--Topical Terms:

682181
Partially ordered sets.

LC Class. No.: QA171.485

Dewey Class. No.: 511.332

Poset codes = partial orders, metrics and coding theory /
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520 $a 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.
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