12 citations · 26 across the 15 of their papers we have counts for
15 papers
Explicit and asymptotically good constructions of Algebraic Geometry codes in the sum-rank metric
Peter Beelen, Elena Berardini, Anina Gruica +1
Algebraic Geometry (AG) codes (i.e. linear codes from algebraic function fields) in the Hamming metric were proposed by Goppa in 1980 and have been intensively studied ever since.…
Locally recoverable codes from elliptic surfaces with availability and hierarchical locality
Elena Berardini, Andrea Fornetto
In this paper, we propose several constructions of Locally Recoverable Codes from elliptic surfaces. In particular, we are able to obtain codes with availability , codes with…
Generalized Skew Multivariate Goppa Codes
Elena Berardini, Pranav Trivedi
We introduce Generalized Skew Multivariate Goppa codes relying on the theory of multivariate Ore polynomials. These codes contain Generalized Skew Goppa codes as a special case. By…
Duality and decoding of linearized Algebraic Geometry codes
Elena Berardini, Xavier Caruso, Fabrice Drain
We design a polynomial time decoding algorithm for linearized Algebraic Geometry codes with unramified evaluation places, a family of sum-rank metric evaluation codes on division a…
A computational approach to Drinfeld modules
Cécile Armana, Elena Berardini, Xavier Caruso +3
This survey provides a practical and algorithmic perspective on Drinfeld modules over . Starting with the construction of the Carlitz module, we present Drinfeld mo…
Asymptotically good CSS-T codes and a new construction of triorthogonal codes
Elena Berardini, Reza Dastbasteh, Josu Etxezarreta Martinez +2
We propose a new systematic construction of CSS-T codes from any given CSS code using a map . When is the identity map , we retrieve the construction of [1] and use it to…
Abelian surfaces over finite fields containing no curves of genus or less
Elena Berardini, Alejandro Giangreco Maidana, Stefano Marseglia
We study abelian surfaces defined over finite fields which do not contain any possibly singular curve of genus less than or equal to . Firstly, we complete and expand the charac…
Reed-Muller codes in the sum-rank metric
Elena Berardini, Xavier Caruso
We introduce the sum-rank metric analogue of Reed--Muller codes, which we called linearized Reed--Muller codes, using multivariate Ore polynomials. We study the parameters of these…
Structure of CSS and CSS-T Quantum Codes
Elena Berardini, Alessio Caminata, Alberto Ravagnani
We investigate CSS and CSS-T quantum error-correcting codes from the point of view of their existence, rarity, and performance. We give a lower bound on the number of pairs of line…
Algebraic Geometry codes in the sum-rank metric
Elena Berardini, Xavier Caruso
We introduce the first geometric construction of codes in the sum-rank metric, which we called linearized Algebraic Geometry codes, using quotients of the ring of Ore polynomials w…
A proof of the Brill-Noether method from scratch
Elena Berardini, Alain Couvreur, Grégoire Lecerf
In 1874 Brill and Noether designed a seminal geometric method for computing bases of Riemann-Roch spaces. From then, their method has led to several algorithms, some of them being…
Curves on Frobenius classical surfaces in over finite fields
Elena Berardini, Jade Nardi
In this paper we give an upper bound on the number of rational points on an irreducible curve of degree defined over a finite field lying on a Frobenius clas…
Weil polynomials of abelian varieties over finite fields with many rational points
Elena Berardini, Alejandro J. Giangreco Maidana
We consider the finite set of isogeny classes of -dimensional abelian varieties defined over the finite field with endomorphism algebra being a field. We prove th…
Bounds on the minimum distance of algebraic geometry codes defined over some families of surfaces
Yves Aubry, Elena Berardini, Fabien Herbaut +1
We prove lower bounds for the minimum distance of algebraic geometry codes over surfaces whose canonical divisor is either nef or anti-strictly nef and over surfaces without irredu…
Algebraic geometry codes over abelian surfaces containing no absolutely irreducible curves of low genus
Yves Aubry, Elena Berardini, Fabien Herbaut +1
We provide a theoretical study of Algebraic Geometry codes constructed from abelian surfaces defined over finite fields. We give a general bound on their minimum distance and we in…