Ferrers Diagram Rank-Metric Codes
Talk by Prof. Dr. Alessandro Neri
Speaker invited by: Prof. Dr. Joachim Rosenthal
Date: 28.05.25 Time: 16.15 - 17.15 Room: Y27H28
Ferrers diagram rank-metric codes were first studied in 2009 by Etzion and Silberstein, motivated by their application in network coding. Concretely, they arise from subspace codes entirely contained in a unique Schubert cell. In their work, the authors proposed a conjecture on the largest dimension of a linear space of matrices over a finite field whose nonzero elements are supported on a given Ferrers diagram and have all rank lower bounded by a fixed positive integer r. Since then, their conjecture has been proved only in some few cases, and as of today it still remains widely open. In this talk, I will give an overview of the main combinatorial and algebraic properties of Ferrers diagram rank-metric codes and on the state of art on the Etzion-Silberstein conjecture, starting from the first findings, until some very recent results.