4 papers
An upper bound for the solving degree in terms of the degree of regularity
Flavio Salizzoni
The solving degree is an important parameter for estimating the complexity of solving a system of polynomial equations. In this paper, we provide an upper bound for the solving deg…
MacWilliams' Extension Theorem for rank-metric codes
Elisa Gorla, Flavio Salizzoni
The MacWilliams' Extension Theorem is a classical result by Florence Jessie MacWilliams. It shows that every linear isometry between linear block-codes endowed with the Hamming dis…
Sum-rank metric codes
Elisa Gorla, Umberto Martínez-Peñas, Flavio Salizzoni
Sum-rank metric codes are a natural extension of both linear block codes and rank-metric codes. They have several applications in information theory, including multishot network co…
Generalized weights of convolutional codes
Elisa Gorla, Flavio Salizzoni
In 1997 Rosenthal and York defined generalized Hamming weights for convolutional codes, by regarding a convolutional code as an infinite dimensional linear code endowed with the Ha…