Rank-Metric Codes Over Finite Rings and Applications

Le séminaire sera en visio : https://univ-rennes1-fr.zoom.us/j/89046973578 (Code secret: 644099).

Rank-metric codes are codes for which each codeword is a matrix and the distance between two codewords is the rank of their difference. Rank-metric codes over finite fields are used in space-time coding, public-key cryptosystems, and random linear network coding. Works on nested-lattice-based network coding suggest the construction of more efficient physical-layer network coding schemes with network coding over finite chain rings. So, finite rings can be used in network coding, but how to detect and correct errors. In this talk, we present the generalization of some results in rank-metric codes to finite commutative principal ideal rings. These results are then applied in network coding and cryptography.