7 papers
A -analogue of the rational normal curve and linearized Reed-Solomon codes
Valentina Astore, Martino Borello, Alain Couvreur +1
The relationship between linear codes in the Hamming metric and projective algebraic varieties has led to deep interactions between coding theory and algebraic geometry, with class…
Benchmarks in Leipzig
Andrei Balakin, Miklós Bóna, Marie-Charlotte Brandenburg +45
Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the 3…
Incidence toric ideals and three-point functions
Barbara Betti, Sean Grate, Thiago Holleben +1
We study the ideal of the algebraic relations among 3-point functions from a combinatorial and topological perspective. We place this problem in the broader setting of incidence to…
The Length of Functional Batch and PIR Codes
Altan B. Kilic, Alberto Ravagnani, Flavio Salizzoni
We consider the problem of computing the minimum length of functional batch and PIR codes of fixed dimension and for a fixed list size, over an arbitrary finite field. We recover,…
A combinatorial description of when a self-associated set of points fails to be arithmetically Gorenstein
Gonzalo RodrÃguez-Pajares, Diego Ruano, Flavio Salizzoni
We prove that the set of points associated to a self-dual code with no proportional columns is arithmetically Gorenstein if and only if the code is indecomposable. This answers a q…
Nonlinear Kalman varieties
Flavio Salizzoni, Luca Sodomaco, Julian Weigert
We study the locus of square matrices having at least one eigenvector on a prescribed algebraic variety . When is a linear subspace, this data locus is known as the Kalman v…