40 citations · 53 across the 12 of their papers we have counts for
14 papers
Locality for Codes over the Integers
Giulia Cavicchioni, Eleonora Guerrini, Julien Lavauzelle
In this work, we study the codes over the integers with locality constraints. We introduce a weighted notion of locality over $\mathbb{Z}/q_1\mathbb{Z} \times \cdots \times \mathbb…
Simultaneous Rational Function Codes: Improved Analysis Beyond Half the Minimum Distance with Multiplicities and Poles
Matteo Abbondati, Eleonora Guerrini, Romain Lebreton
In this paper, we extend the work of Abbondati et al. (2024) on decoding simultaneous rational function codes by addressing two important scenarios: multiplicities and poles (zeros…
Simultaneous Rational Number Codes: Decoding Beyond Half the Minimum Distance with Multiplicities and Bad Primes
Matteo Abbondati, Eleonora Guerrini, Romain Lebreton
In this paper, we extend the work of (Abbondati et al., 2024) on decoding simultaneous rational number codes by addressing two important scenarios: multiplicities and the presence…
A class of locally recoverable codes over finite chain rings
Giulia Cavicchioni, Eleonora Guerrini, Alessio Meneghetti
Locally recoverable codes deal with the task of reconstructing a lost symbol by relying on a portion of the remaining coordinates smaller than an information set. We consider the c…
Polynomial Linear System Solving with Random Errors: new bounds and early termination technique
Guerrini Eleonora, Lebreton Romain, Zappatore Ilaria
This paper deals with the polynomial linear system solving with errors (PLSwE) problem. Specifically, we focus on the evaluation-interpolation technique for solving polynomial line…
Enhancing simultaneous rational function recovery: adaptive error correction capability and new bounds for applications
Eleonora Guerrini, Romain Lebreton, Ilaria Zappatore
In this work we present some results that allow to improve the decoding radius in solving polynomial linear systems with errors in the scenario where errors are additive and random…
On the Uniqueness of Simultaneous Rational Function Reconstruction
Eleonora Guerrini, Romain Lebreton, Ilaria Zappatore
This paper focuses on the problem of reconstructing a vector of rational functions given some evaluations, or more generally given their remainders modulo different polynomials. Th…
Polynomial Linear System Solving with Errors by Simultaneous Polynomial Reconstruction of Interleaved Reed-Solomon Codes
E. Guerrini, R. Lebreton, I. Zappatore
In this paper we present a new algorithm for Polynomial Linear System Solving (via evaluation/interpolation) with errors. In this scenario, errors can occur in the black box evalua…
On optimal nonlinear systematic codes
Eleonora Guerrini, Alessio Meneghetti, Massimiliano Sala
Most bounds on the size of codes hold for any code, whether linear or not. Notably, the Griesmer bound holds only in the linear case and so optimal linear codes are not necessarily…
On the Griesmer bound for nonlinear codes
Emanuele Bellini, Eleonora Guerrini, Alessio Meneghetti +1
Most bounds on the size of codes hold for any code, whether linear or nonlinear. Notably, the Griesmer bound, holds only in the linear case. In this paper we characterize a family…
Some bounds on the size of codes
Emanuele Bellini, Eleonora Guerrini, Massimiliano Sala
We present some upper bounds on the size of non-linear codes and their restriction to systematic codes and linear codes. These bounds are independent of other known theoretical bou…
Extremal graphs for the identifying code problem
Florent Foucaud, Eleonora Guerrini, Matjaz Kovse +3
An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from all other vertices by the set of vertices in C that are at distance at mo…
Computing the distance distribution of systematic non-linear codes
Eleonora Guerrini, Emmanuela Orsini, Massimiliano Sala
The most important families of non-linear codes are systematic. A brute-force check is the only known method to compute their weight distribution and distance distribution. On the…
A bound on the size of linear codes
Eleonora Guerrini, Massimiliano Sala
We present a bound on the size of linear codes. This bound is independent of other known bounds, e.g. the Griesmer bound.