Algebraic Methods in Coding Theory and Communication (20w5187)


(Clemson University)

(University of Neuchatel)

Marcus Greferath (Aalto University)

Hiram H. López Valdez (Autonomous University of Aguascalientes)


The Casa Matemática Oaxaca (CMO) will host the "Algebraic Methods in Coding Theory and Communication" workshop in Oaxaca, from October 25 to October 30, 2020.

Since the seminal works of Claude Shannon in the 1940's, coding theory has been a flourishing subject for research collaborations between mathematicians, computer scientists and electrical engineers. Research problems in coding theory have evolved in the years to answer important practical questions from real world applications. This workshop aims at bringing together researchers from different backgrounds in order to foster interdisciplinary collaborations that will push forward the research in coding theory and communication.

The workshop will concentrate on three contemporary, central themes in coding theory and its applications. Algebraic coding theory tackles classical communication problems, such as error-free communication between a source and a receiver over a noisy channel, using a wide range of tools from computational algebra, algebraic geometry, and probability theory. More recently coding theory has found applications to emerging challenges in communication. The kind of problems that arise has been shifting, as our digital lives got more and more interconnected. Network Coding seeks answers to problems of maximization of information flow over networks. These answers often require establishing new communication schemes, relying on mathematical structures which were not used in this context before. In the last few years a new set of problems with local features arose from practical applications such as distributed storage of large amounts of data. Locally recoverable codes allow the recovery of a codeword symbol's erasure by mean of a small set of other codeword symbols. These codes are a central topic of research of the last few years, due also to their applicability to these problems.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT