Together with Marco Timpanella (University of Perugia) and Giovanni Zini (University of Modena and Reggio Emilia), the research group organize monthly seminars.
21 May 2026 [4.00 pm - Italian time] - Valentina Astore (INRIA Center - Paris)
Title: The Geometry of Linearized Reed-Solomon Codes
Abstract: Linearized Reed–Solomon (LRS) codes naturally generalize both Reed–Solomon and Gabidulin codes, and sit at the intersection of the Hamming and rank metrics via the sum-rank metric. While Reed–Solomon and Gabidulin codes admit both algebraic and geometric descriptions, no general method is known to identify the structure of an LRS code. Existing approaches are not fully general and typically require recovering partial information about the code parameters before analyzing its structure.
In this talk, we propose a geometric perspective to study LRS codes. We begin by describing the structural properties of the geometric object associated with these codes and show how it relates to a q-analogue of the rational normal curve. Through this interpretation, we obtain a geometric characterization of LRS codes that yields an effective method to identify them for certain ranges of parameters. Finally, we conclude by investigating the Hilbert function of LRS codes, focusing in particular on its Hilbert regularity.