EAN: 9783319938202

SPRINGERBRIEFS IN MATHEMATICS POSET CODES PAR...

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.

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