Poset Codes: Partial Orders, Metrics and Coding Theory

This book provides an organized and systematic approach to poset metrics and codes, covering basic concepts of coding theory and advancing to coding theory for poset metrics and generalizations. It is designed to be self-contained and will appeal to researchers and graduate students in Mathematics, Electrical Engineering, and Computer Sciences.

Format: Paperback / softback
Length: 127 pages
Publication date: 13 November 2018
Publisher: Springer International Publishing AG

This comprehensive book provides a thorough and systematic exploration of poset metrics and codes. Poset metrics, also known as metrics on a vector field defined by a partial order over a finite set, were first introduced in the mid-1990s by renowned mathematicians Richard A. Brualdi, Janine S. Graves, and K. Mark Lawrence. Since then, the field has witnessed an extensive accumulation of knowledge, with over two hundred research papers dedicated to this topic. Poset metrics offer a powerful generalization of both the standard Hamming metric, widely used in coding theory, and the Niederreiter-Rosenbloom-Tsfasman metric, known as an ultrametric. The book aims to be as self-contained as possible, starting from fundamental concepts of coding theory and progressing to the application of poset metrics and generalizations. Each chapter includes a comprehensive survey of the discussed topic, accompanied by a comprehensive list of exercises. These exercises are drawn from recently proven results, ensuring that readers have access to the latest developments in the field. This work is of immense interest to researchers and graduate students alike, particularly those specializing in Mathematics, Electrical Engineering, and Computer Sciences. Those with a passion for discrete geometry and coding theory will find this book to be a valuable resource.

Weight: 207g
Dimension: 234 x 156 x 7 (mm)
ISBN-13: 9783319938202
Edition number: 1st ed. 2018