20 citations · 25 across the 6 of their papers we have counts for
7 papers
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…
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…
Power Series Solutions of Singular (q)-Differential Equations
Alin Bostan, Muhammad F. I. Chowdhury, Romain Lebreton +2
We provide algorithms computing power series solutions of a large class of differential or -differential equations or systems. Their number of arithmetic operations grows linear…