Poset Codes: Partial Orders, Metrics and Coding Theory

Marcelo Firer holds Bachelor's (1989) and Master's (1991) degrees in Mathematics from the University of Campinas (Unicamp), Brazil, and received his PhD in Mathematics from the Hebrew University of Jerusalem (1997), Israel, under the supervision of Dr. Ilya Rips. He is currently a researcher at the Department of Mathematics at Unicamp, where he has worked since 1999. During this period his research focus has shifted from differential geometry and symmetric spaces to discrete geometrical problems in the context of Coding Theory. Marcelo Muniz S. Alves completed his Bachelor's (1996), Master's (1998) and PhD (2002) studies in Mathematics at the University of Campinas (Unicamp), Brazil. In 2002 he joined the Department of Mathematics at the Federal University of Paraná (UFPR), Brazil, where he works as an Associate Professor. His current research is focused on poset codes and, in particular, codes in the Rosenbloom-Tsfasman metric. In addition, he is pursuing research on actions and representations of Hopf algebras. Jerry Anderson Pinheiro holds a Master's degree (2011) and a PhD (2016), both in Mathematics, from the University of Campinas (Unicamp), Brazil, (2016), with studies at the University College Dublin, Claude Shannon Institute, Ireland (2013). His research interests lie in combinatorics, coding theory, discrete geometry and information theory. Luciano Panek is a professor at the State University of West Paraná, Brazil. He received his Bachelor's and PhD degrees from the State University of Maringá, Brazil, in 2000 and 2012, respectively, both in Mathematics, and his Master's degree in Mathematics (2003) from the University of Campinas, Brazil. His research fields include error-correcting codes, information theory and discrete 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.

"The book's contents are well chosen and well structured, and the book is accessible and easy to read. ... this is an excellent exposition on poset codes and will undoubtedly be used both as a work of reference for researchers and as a course book for undergraduate students." (Thomas Britz, Mathematical Reviews, July, 2019)
"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." (M. M. Tanik, Computing Reviews, October 17, 2019)