Codes Endowed with the Rank Metric
Alberto Ravagnani (Université de Neuchâtel)
Network coding is a novel research field in the panorama of coding theory that comes as an answer to the problem of efficient and reliable transmissions over networks. The typical scenario within network coding consists of one source of information that attempts to transmit certain messages to several receivers via a network of intermediate nodes.
Rank-metric codes play a crucial role in the context of network transmissions, as they allow to correct errors and erasures that may occur at the intermediate nodes of the network.
In my talk I will discuss the most important properties of codes endowed with the rank-metric, and present the algebraic parameters that describe their performance in the context of network transmissions (e.g. the minimum rank distance and the rank distribution). I will then introduce quasi-MRD rank-metric codes, and present some new results on their rank distribution.
Alberto Ravagnani was born in Verona, Italy, in 1988. He received the BSc and MSc degree in Mathematics from the University of Trento (Italy) in 2010 and 2012 respectively. He is currently doctoral student in Mathematics at the University of Neuchâtel, Switzerland. The research interests of Alberto Ravagnani are in Coding Theory (Network Coding in particular). Since 2013 he is Member of the Society of Industrial and Applied Mathematics (SIAM).
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