44 citations · 63 across the 24 of their papers we have counts for
14 papers · 1 filter
Code distances of matrix rank-metric codes under Add-and-Remove transformations
Gianira N. Alfarano, Rakhi Pratihar, Adrien Vinçotte
For a matrix rank-metric code and an integer , the -th subcode distance of is the largest minimum rank distance of an -dimensional subcode of $…
A proof of the generalized packing-covering conjecture
Gianira N. Alfarano, Giuseppe Marino, Alessandro Neri +1
The generalized packing--covering conjecture of Elimelech, Firer and Schwartz asserts that, for every linear code and every admissible order , the -th generaliz…
Minimal additive codes and additive strong blocking sets
Gianira N. Alfarano, Marine Le Meur
Additive codes over generalize linear codes by relaxing linearity over the alphabet while retaining linearity over the subfield . In this paper, we…
Schubert Subspace Codes
Gianira N. Alfarano, Joachim Rosenthal, Beatrice Toesca
In this paper, we initiate the study of constant dimension subspace codes restricted to Schubert varieties, which we call Schubert subspace codes. These codes have a very natural g…
Dual-Code Bounds on Multiple Concurrent (Local) Data Recovery
Gianira N. Alfarano, Alberto Ravagnani, Emina Soljanin
We are concerned with linear redundancy storage schemes regarding their ability to provide concurrent (local) recovery of multiple data objects. This paper initiates a study of suc…
Sum-rank product codes and bounds on the minimum distance
Gianira N. Alfarano, F. J. Lobillo, Alessandro Neri +1
The tensor product of one code endowed with the Hamming metric and one endowed with the rank metric is analyzed. This gives a code which naturally inherits the sum-rank metric. Spe…
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…
Weighted Reed-Solomon convolutional codes
Gianira N. Alfarano, Diego Napp, Alessandro Neri +1
In this paper we present a concrete algebraic construction of a novel class of convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be…
Construction of LDPC convolutional codes via difference triangle sets
Gianira N. Alfarano, Julia Lieb, Joachim Rosenthal
In this paper, a construction of LDPC convolutional codes over arbitrary finite fields, which generalizes the work of Robinson and Bernstein and the later work of Tong is…
On single server private information retrieval in a coding theory perspective
Gianira N. Alfarano, Karan Khathuria, Violetta Weger
In this paper, we present a new perspective of single server private information retrieval (PIR) schemes by using the notion of linear error-correcting codes. Many of the known sin…
On the left primeness of some polynomial matrices with applications to convolutional codes
Gianira N. Alfarano, Julia Lieb
Maximum distance profile (MDP) convolutional codes have the property that their column distances are as large as possible for given rate and degree. There exists a well-known crite…
Roos bound for skew cyclic codes in Hamming and rank metric
Gianira N. Alfarano, F. J. Lobillo, Alessandro Neri
In this paper, a Roos like bound on the minimum distance for skew cyclic codes over a general field is provided. The result holds in the Hamming metric and in the rank metric. The…
Construction of Rate (n-1)/n Non-Binary LDPC Convolutional Codes via Difference Triangle Sets
Gianira N. Alfarano, Julia Lieb, Joachim Rosenthal
This paper provides a construction of non-binary LDPC convolutional codes, which generalizes the work of Robinson and Bernstein. The sets of integers forming an -differenc…
A geometric characterization of minimal codes and their asymptotic performance
Gianira Nicoletta Alfarano, Martino Borello, Alessandro Neri
In this paper, we give a geometric characterization of minimal linear codes. In particular, we relate minimal linear codes to cutting blocking sets, introduced in a recent paper by…