Diego Napp
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View article: Easy repair via codes with simplex locality
Easy repair via codes with simplex locality Open
In the context of distributed storage systems, locally repairable codes have become important. In this paper we focus on codes that allow for multi-erasure pattern decoding with low computational effort. Different optimality requirements, …
View article: Superregular Matrices over Finite Fields
Superregular Matrices over Finite Fields Open
A trivially zero minor of a matrix is a minor having all its terms in the Leibniz formula equal to zero. A matrix is superregular if all of its minors that are not trivially zero are nonzero. In the area of Coding Theory, superregular matr…
View article: On the construction of MRD convolutional codes
On the construction of MRD convolutional codes Open
The problem of building optimal block codes, such as MDS codes, over small fields has been an active area of research that led to several interesting conjectures. In the context of convolutional codes, optimal constructions, such as MDS or…
View article: Weighted Reed–Solomon convolutional codes
Weighted Reed–Solomon convolutional codes Open
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 seen as a natural extension of Reed–Solomon block codes to…
View article: Weight-2 input sequences of $ 1/n $ convolutional codes from linear systems point of view
Weight-2 input sequences of $ 1/n $ convolutional codes from linear systems point of view Open
Convolutional codes form an important class of codes that have memory. One natural way to study these codes is by means of input state output representations. In this paper we study the minimum (Hamming) weight among codewords produced by …
View article: State-Space Realizations of Periodic Convolutional Codes
State-Space Realizations of Periodic Convolutional Codes Open
Convolutional codes are discrete linear systems over a finite field and can be defined as F[d]-modules, where F[d] is the ring of polynomials with coefficient in a finite field F. In this paper we study the algebraic properties of periodic…
View article: Noncatastrophic convolutional codes over a finite ring
Noncatastrophic convolutional codes over a finite ring Open
Noncatastrophic encoders are an important class of polynomial generator matrices of convolutional codes. When these polynomials have coefficients in a finite field, these encoders have been characterized as polynomial left prime matrices. …
View article: Minimal State-Space Representation of Convolutional Product Codes
Minimal State-Space Representation of Convolutional Product Codes Open
In this paper, we study product convolutional codes described by state-space representations. In particular, we investigate how to derive state-space representations of the product code from the horizontal and vertical convolutional codes.…
View article: Smaller Keys for Code-Based Cryptography: McEliece Cryptosystems with Convolutional Encoders.
Smaller Keys for Code-Based Cryptography: McEliece Cryptosystems with Convolutional Encoders. Open
In this paper we present a novel class of convolutional codes and investigate its use in a variant of the McEliece cryptosystem that possesses several interesting properties, including a reduction of the public key for a given security lev…
View article: Smaller Keys for the McEliece Cryptosystem: A Convolutional Variant with GRS Codes
Smaller Keys for the McEliece Cryptosystem: A Convolutional Variant with GRS Codes Open
In this paper we present a variant of the McEliece cryptosystem that possesses several interesting properties, including a reduction of the public key for a given security level. In contrast to the classical McEliece cryptosystems, where b…
View article: Weighted Reed-Solomon convolutional codes
Weighted Reed-Solomon convolutional codes Open
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 seen as a natural extension of Reed-Solomon block codes to…
View article: Superregular matrices over small finite fields
Superregular matrices over small finite fields Open
A trivially zero minor of a matrix is a minor having all its terms in the Leibniz formula equal to zero. A matrix is superregular if all of its minors that are not trivially zero are nonzero. In the area of Coding Theory, superregular matr…
View article: Generalized Column Distances
Generalized Column Distances Open
The notion of Generalized Hamming weights of block codes has been investigated since the nineties due to its significant role in coding theory and cryptography. In this paper we extend this concept to the context of convolutional codes. In…
View article: Locally Repairable Convolutional Codes With Sliding Window Repair
Locally Repairable Convolutional Codes With Sliding Window Repair Open
Locally repairable convolutional codes (LRCCs) for distributed storage systems (DSSs) are introduced in this work. They enable local repair, for a single node erasure (or more generally, ∂−1 erasures per local group), and sliding-window gl…
View article: Robust low-delay Streaming PIR using convolutional codes
Robust low-delay Streaming PIR using convolutional codes Open
In this paper we investigate the design of a low-delay robust streaming PIR scheme on coded data that is resilient to unresponsive or slow servers and can privately retrieve streaming data in a sequential fashion subject to a fixed decodin…
View article: Realization of 2D (2,2)–Periodic Encoders by Means of 2D Periodic Separable Roesser Models
Realization of 2D (2,2)–Periodic Encoders by Means of 2D Periodic Separable Roesser Models Open
It is well known that convolutional codes are linear systems when they are defined over a finite field. A fundamental issue in the implementation of convolutional codes is to obtain a minimal state representation of the code. Compared with…
View article: Column Distances of Convolutional Codes Over <inline-formula> <tex-math notation="LaTeX">${\mathbb Z}_{p^r}$ </tex-math> </inline-formula>
Column Distances of Convolutional Codes Over Open
Maximum distance profile codes over finite nonbinary fields have been introduced and thoroughly studied in the last decade. These codes have the property that their column distances are maximal among all codes of the same rate and degree. …
View article: Faster decoding of rank metric convolutional codes
Faster decoding of rank metric convolutional codes Open
A new construction of maximum rank distance systematic rank metric convolutional codes is presented, which permits to reduce the computational complexity of the decoding procedure, i.e., of the underlying Viterbi algorithm. This result is …
View article: On the state space realization of 2D (2,2)-periodic image behaviors
On the state space realization of 2D (2,2)-periodic image behaviors Open
In this paper we consider 2D behaviors with periodic image representations and provide conditions under which a simple method for obtaining state space realizations by means of 2D periodic (separable) Roesser models can be applied. For the…
View article: A new class of convolutional codes and its use in the McEliece Cryptosystem
A new class of convolutional codes and its use in the McEliece Cryptosystem Open
In this paper we present a new class of convolutional codes that admits an efficient al- gebraic decoding algorithm. We study some of its properties and show that it can decode interesting sequences of errors patterns. The second part of t…
View article: Column distance of convolutional codes over Zpr
Column distance of convolutional codes over Zpr Open
Rosenthal et al. introduced and thoroughly studied the notion of Maximum Distance Profile (MDP) convolutional codes over (non-binary) finite fields refining the classical notion of optimum distance profile, see for instance [18, p.164]. Th…
View article: Generalized column distances for convolutional codes
Generalized column distances for convolutional codes Open
In this work, we adapt the notion of generalized Hamming weight of block codes to introduce the novel concept of generalized column distances for convolutional codes. This can be considered as an extension of the work done in [18] on the g…
View article: Rank metric convolutional codes
Rank metric convolutional codes Open
In this contribution, we propose a first general definition of rank-metric convolutional codes for multi-shot network coding. To this aim, we introduce a suitable concept of distance and we establish a generalized Singleton bound for this …
View article: Constructing strongly-MDS convolutional codes with maximum distance profile
Constructing strongly-MDS convolutional codes with maximum distance profile Open
This paper revisits strongly-MDS convolutional codes with maximum distance profile (MDP). These are (non-binary) convolutional codes that have an optimum sequence of column distances and attains the generalized Singleton bound at the earli…