PhD Defense by Umberto Martinez-Penas


13.11.2017 kl. 13.00 - 13.11.2017 kl. 17.00


Topics on Reliable and Secure Communication using Rank-Metric and Classical Linear Codes By Umberto Martinez-Penas

Rank-metric codes play a central role in reliable and secure communications in different practical settings, such as linear network coding or storage systems with crisscross errors. The behaviour of rank-metric codes is in many cases analogous to that of Hamming-metric codes. However, there exist numerous cases where rank-metric codes present unexpected properties with no analogy in the Hamming case. In this thesis, we explore the similarities and differences between rank-metric codes and Hamming-metric codes and, from this analysis, we provide new applications in the previously mentioned settings. The results and papers in this thesis fall into three categories:

First, we study rank-metric nested code pairs and their relative generalized weights. These parameters measure the security performance of the corresponding code pairs in linear network coding.

Second, we study skew cyclic codes seen as rank-metric codes. We provide bounds on their parameters, study their structure and provide decoding algorithms.

Third, we study the asymptotic behaviour of sequences of secret sharing schemes, and provide new algebraic tools for further studies on reliable and secure communications.

Bedømmelsesudvalg/Assessment committee:

Adjungeret Professor Tom Høholdt, Aalborg Universitet
Professor Chaoping Xing, Nanyang Technological University
Professor Joachim Rosenthal, University of Zürich


Institutleder/Head of Department Søren Højsgaard


Professor Olav Geil
Lektor/Associate professor Diego Ruano



Institut for Matematiske Fag


Skjernvej 4A, rum 5.034

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07.11.2017 kl. 12.00

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