12 citations · 26 across the 15 of their papers we have counts for
7 papers · 1 filter
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…
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 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…