21 papers
A Matroidal Framework for Random Access in Linear Codes
Daniella Bar-Lev, Hiram H. López, Gretchen L. Matthews +1
We study random access in linear codes when codeword symbols are sampled independently and uniformly with replacement. A code is recovery balanced if the expected number of samples…
Quantum Matrix-Product Codes: CSS-T Characterization and Maximality
Delio Jaramillo-Velez, Alessandro Neri, Adway Patra +2
CSS-T codes are quantum error-correcting codes that play an important role in fault-tolerant quantum computation, as they help mitigate the proliferation of errors. They admit a tr…
Generalized Hamming weights of codes arising from complete intersection
Eduardo Camps Moreno, Flavio Salizzoni, Rodrigo San-José
We provide a positive answer to a conjecture proposed by Tohǎneanu and Van Tuyl regarding the minimum distance of codes whose underlying set of points is a reduced complete interse…
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 t…
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…
A combinatorial description of when a self-associated set of points fails to be arithmetically Gorenstein
Gonzalo Rodríguez-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…
Nonlinear Rayleigh quotient optimization
Flavio Salizzoni, Luca Sodomaco, Julian Weigert
Rayleigh quotient minimization deals with optimizing a quadratic homogeneous function over a sphere. Its critical points correspond to the normalized eigenvectors of the symmetric…
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,…
Latroids and code invariants
Elisa Gorla, Flavio Salizzoni
Latroids were introduced by Vertigan, who associated a latroid to a linear block code and showed that its Tutte polynomial determines the weight enumerator of the code. The origina…
A geometric invariant of linear rank-metric codes
Valentina Astore, Martino Borello, Marco Calderini +1
Rank-metric codes have been a central topic in coding theory due to their theoretical and practical significance, with applications in network coding, distributed storage, crisscro…
Integer sequences that are generalized weights of a linear code
Elisa Gorla, Elisa Lorenzo García, Umberto Martínez-Peñas +1
Which integer sequences are sequences of generalized weights of a linear code? In this paper, we answer this question for linear block codes, rank-metric codes, and more generally…
An upper bound for the solving degree in terms of the degree of regularity
Flavio Salizzoni
The solving degree is an important parameter for estimating the complexity of solving a system of polynomial equations. In this paper, we provide an upper bound for the solving deg…
MacWilliams' Extension Theorem for rank-metric codes
Elisa Gorla, Flavio Salizzoni
The MacWilliams' Extension Theorem is a classical result by Florence Jessie MacWilliams. It shows that every linear isometry between linear block-codes endowed with the Hamming dis…
Sum-rank metric codes
Elisa Gorla, Umberto Martínez-Peñas, Flavio Salizzoni
Sum-rank metric codes are a natural extension of both linear block codes and rank-metric codes. They have several applications in information theory, including multishot network co…
Generalized column distances
Elisa Gorla, Flavio Salizzoni
We define a notion of r-generalized column distances for the j-truncation of a convolutional code. Taking the limit as j tends to infinity allows us to define r-generalized column…
Generalized weights of convolutional codes
Elisa Gorla, Flavio Salizzoni
In 1997 Rosenthal and York defined generalized Hamming weights for convolutional codes, by regarding a convolutional code as an infinite dimensional linear code endowed with the Ha…
Optimal anticodes, MSRD codes, and generalized weights in the sum-rank metric
Eduardo Camps Moreno, Elisa Gorla, Cristina Landolina +3
Sum-rank metric codes have recently attracted the attention of many researchers, due to their relevance in several applications. Mathematically, the sum-rank metric is a natural ge…
Additivity of the algebraic entropy for locally finite groups with permutable finite subgroups
Anna Giordano Bruno, Flavio Salizzoni
The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exp…
The addition theorem for locally monotileable monoid actions
Dikran Dikranjan, Antongiulio Fornasiero, Anna Giordano Bruno +1
We prove an instance of the so-called Addition Theorem for the algebraic entropy of actions of cancellative right amenable monoids on discrete abelian groups by endomorphis…