Zobrazeno 1 - 10
of 157
pro vyhledávání: '"Gorla, Elisa"'
Autor:
Gaggero, Giulia, Gorla, Elisa
A multivariate cryptograpic instance in practice is a multivariate polynomial system. So the security of a protocol rely on the complexity of solving a multivariate polynomial system. In this paper there is an overview on a general algorithm used to
Externí odkaz:
http://arxiv.org/abs/2309.03855
Which integer sequences are sequences of generalized weights of a linear code? In this paper, we answer this question for linear block codes, rank-metric codes, and more generally for sum-rank metric codes. We do so under an existence assumption for
Externí odkaz:
http://arxiv.org/abs/2307.06595
Autor:
Gorla, Elisa, Salizzoni, Flavio
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 distance can be extended to a linear isometry of the ambient space. Such
Externí odkaz:
http://arxiv.org/abs/2304.13341
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 coding and distributed storage systems. The aim of this chapter is to pr
Externí odkaz:
http://arxiv.org/abs/2304.12095
Autor:
Gorla, Elisa, Salizzoni, Flavio
We define a notion of r-generalized column distances for the j-truncation of a convolutional code. Taking the limit as j tends to infinity allows us to define r-generalized column distances of a convolutional code. We establish some properties of the
Externí odkaz:
http://arxiv.org/abs/2212.12265
Autor:
Gorla, Elisa, Salizzoni, Flavio
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 Hamming metric. In this paper, we propose a new definition of generalize
Externí odkaz:
http://arxiv.org/abs/2207.12170
Can one tell if an ideal is radical just by looking at the degrees of the generators? In general, this is hopeless. However, there are special collections of degrees in multigraded polynomial rings, with the property that any multigraded ideal genera
Externí odkaz:
http://arxiv.org/abs/2203.08732
Autor:
Gorla, Elisa, Landolina, Cristina
It is well-known that the dimension of optimal anticodes in the rank-metric is divisible by the maximum m between the number of rows and columns of the matrices. Moreover, for a fixed k divisible by m, optimal rank-metric anticodes are the codes with
Externí odkaz:
http://arxiv.org/abs/2201.07579
Autor:
Gorla, Elisa, Ravagnani, Alberto
We develop an algebraic theory of supports for $R$-linear codes of fixed length, where $R$ is a finite commutative unitary ring. A support naturally induces a notion of generalized weights and allows one to associate a monomial ideal to a code. Our m
Externí odkaz:
http://arxiv.org/abs/2201.05813
The solving degree of a system of multivariate polynomial equations provides an upper bound for the complexity of computing the solutions of the system via Groebner bases methods. In this paper, we consider polynomial systems that are obtained via We
Externí odkaz:
http://arxiv.org/abs/2112.10506