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# AGNT – Anna-Lena Trautmann – EPF Lausanne, Switzerland

## October 17, 2016 @ 3:30 pm - 4:30 pm

**Linearized polynomial modules and their application to network coding**

Linearized polynomials are a certain family of polynomials over finite fields. They form a non-commutative ring with the two operations addition and composition. In this ring we will consider special modules of rank 2, which we call interpolation modules, and determine minimal (GrÃ¶bner) bases of these modules. Furthermore we give a brief introduction to network coding and show how linearized polynomials are used to construct optimal rank-metric codes, also called Gabidulin codes. In the network coding setting, the problem of decoding such a code can be translated to a parametrization based on a minimal basis of the interpolation module. We conclude our talk by explaining the parametrization and the decoding algorithm, and determining the complexity order of it.