Title: Length-metric codes

 Abstract: 

We will talk about length-metric codes, a new variant of error-correcting code that we developed as an algebraic proxy for submodule codes used in physical-layer network coding, which were introduced by Gorla and Ravagnani. We will briefly summarise the history and importance of error-correcting codes in information theory, using perhaps the most well-known error-correcting codes, namely Hamming codes, as an example. We will then mention rank-metric codes and use the latter two examples to motivate some of the main problems of coding theory. Finally, we will introduce length-metric codes, which not only model submodule codes but generalise rank-metric codes. In particular, we will discuss code equivalence, optimal codes and local-to-global arguments in the length-metric. This is joint work with Elisa Gorla.

https://www.unine.ch/math/seminaire-algebre-et-geometrie-de-neuchatel/