7 citations · 11 across the 15 of their papers we have counts for
22 papers
Sunflowers of Reed--Solomon Codes
Roni Con, Anina Gruica, Maria Montanucci +1
We introduce and study Reed--Solomon sunflowers, namely families of Reed--Solomon codes whose pairwise intersections are all equal to the same fixed subspace. This notion lies at t…
The Generalized Random Access Problem for Linear Codes
Anina Gruica, Antonio Petrillo, Ferdinando Zullo
Random access is a central requirement in DNA-based storage systems: one would like to recover selected information symbols without sequencing the whole encoded object. A recent co…
Linear Code Conversion in the Merge Regime: General Bounds and Reed-Muller Constructions
Anina Gruica, Benjamin Jany, Stanislav Kruglik
Erasure codes are a core component of most existing large-scale distributed storage systems, ensuring reliability against node failures. Recent work has shown that adapting code pa…
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.…
Convertible Codes for Data and Device Heterogeneity
Anina Gruica, Benjamin Jany, Stanislav Kruglik
Distributed storage systems must handle both data heterogeneity, arising from non-uniform access demands, and device heterogeneity, caused by time-varying node reliability. In this…
Serving Every Symbol: All-Symbol PIR and Batch Codes
Avital Boruchovsky, Anina Gruica, Jonathan Niemann +1
A -all-symbol PIR code and a -all-symbol batch code of dimension consist of servers storing linear combinations of information symbols with the following recovery…
Making it to First: The Random Access Problem in DNA Storage
Avital Boruchovsky, Ohad Elishco, Ryan Gabrys +3
In this paper, we study the Random Access Problem in DNA storage, which addresses the challenge of retrieving a specific information strand from a DNA-based storage system. In this…
Reed-Solomon Codes Against Insertions and Deletions: Full-Length and Rate- Codes
Peter Beelen, Roni Con, Anina Gruica +2
The performance of Reed--Solomon codes (RS codes, for short) in the presence of insertion and deletion errors has attracted growing attention in recent literature. In this work, we…
The Geometry of Codes for Random Access in DNA Storage
Anina Gruica, Maria Montanucci, Ferdinando Zullo
Effective and reliable data retrieval is critical for the feasibility of DNA storage, and the development of random access efficiency plays a key role in its practicality and relia…
Achieving DNA Labeling Capacity with Minimum Labels through Extremal de Bruijn Subgraphs
Christoph Hofmeister, Anina Gruica, Dganit Hanania +2
DNA labeling is a tool in molecular biology and biotechnology to visualize, detect, and study DNA at the molecular level. In this process, a DNA molecule is labeled by a set of spe…
A Combinatorial Perspective on Random Access Efficiency for DNA Storage
Anina Gruica, Daniella Bar-Lev, Alberto Ravagnani +1
We investigate the fundamental limits of the recently proposed random access coverage depth problem for DNA data storage. Under this paradigm, it is assumed that the user informati…
Rank-Metric Codes and Their Parameters
Anina Gruica, Altan B. Kilic, Alberto Ravagnani
We present the theory of linear rank-metric codes from the point of view of their fundamental parameters. These are: the minimum rank distance, the rank distribution, the maximum r…
The Diagonals of a Ferrers Diagram
Giuseppe Cotardo, Anina Gruica, Alberto Ravagnani
We propose and develop a theory of Ferrers diagrams and their -rook polynomials solely based on their diagonals. We show that the cardinalities of the diagonals of a Ferrers dia…
LRCs: Duality, LP Bounds, and Field Size
Anina Gruica, Benjamin Jany, Alberto Ravagnani
We develop a duality theory of locally recoverable codes (LRCs) and apply it to establish a series of new bounds on their parameters. We introduce and study a refined notion of wei…
Duality and LP Bounds for Codes with Locality
Anina Gruica, Benjamin Jany, Alberto Ravagnani
We initiate the study of the duality theory of locally recoverable codes, with a focus on the applications. We characterize the locality of a code in terms of the dual code, and in…
Rook Theory of the Etzion-Silberstein Conjecture
Anina Gruica, Alberto Ravagnani
In 2009, Etzion and Siberstein proposed a conjecture on the largest dimension of a linear space of matrices over a finite field in which all nonzero matrices are supported on a Fer…
Densities of Codes of Various Linearity Degrees in Translation-Invariant Metric Spaces
Anina Gruica, Anna-Lena Horlemann, Alberto Ravagnani +1
We investigate the asymptotic density of error-correcting codes with good distance properties and prescribed linearity degree, including sublinear and nonlinear codes. We focus on…
Generalised Evasive Subspaces
Anina Gruica, Alberto Ravagnani, John Sheekey +1
We introduce and explore a new concept of evasive subspace with respect to a collection of subspaces sharing a common dimension, most notably partial spreads. We show that this con…
Rank-Metric Codes, Semifields, and the Average Critical Problem
Anina Gruica, Alberto Ravagnani, John Sheekey +1
We investigate two fundamental questions intersecting coding theory and combinatorial geometry, with emphasis on their connections. These are the problem of computing the asymptoti…
The Typical Non-Linear Code over Large Alphabets
Anina Gruica, Alberto Ravagnani
We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Ha…
Convolutional codes over finite chain rings, MDP codes and their characterization
Gianira N. Alfarano, Anina Gruica, Julia Lieb +1
In this paper, we develop the theory of convolutional codes over finite commutative chain rings. In particular, we focus on maximum distance profile (MDP) convolutional codes and w…
Common Complements of Linear Subspaces and the Sparseness of MRD Codes
Anina Gruica, Alberto Ravagnani
Motivated by applications to the theory of rank-metric codes, we study the problem of estimating the number of common complements of a family of subspaces over a finite field in te…