1,721,084 research outputs found
La componente educativa nella cura di pazienti con disturbo del comportamento alimentare
No full textLa cura dei Disturbi del Comportamento Alimentare, secondo le linee guidanazionali ed internazionali, deve coinvolgere diverse figure professionali e deve rivolgersi ai diversi aspetti della psicopatologia alimentare. La psicoeducazione rappresenta un importante passo in ogni programma terapeutico di questi disturbi dall'eziologia complessa
Linearized trinomials with maximum kernel
No full textLinearized polynomials have attracted a lot of attention because of their applications in both geometric and algebraic areas. Let q be a prime power, n be a positive integer and σ be a generator of Gal(Fqjavax.xml.bind.JAXBElement@226d5689:Fq). In this paper we provide closed formulas for the coefficients of a σ-trinomial f over Fqjavax.xml.bind.JAXBElement@4cee590e which ensure that the dimension of the kernel of f equals its σ-degree, that is linearized polynomials with maximum kernel. As a consequence, we present explicit examples of linearized trinomials with maximum kernel and characterize those having σ-degree 3 and 4. Our techniques rely on the tools developed in [24]. Finally, we apply these results to investigate a class of rank metric codes introduced in [8], to construct quasi-subfield polynomials and cyclic subspace codes, obtaining new explicit constructions to the conjecture posed in [37]
On the list decodability of rank-metric codes containing Gabidulin codes
No full textWachter-Zeh (IEEE Trans Inf Theory 59(11):7268–7276, 2013), and later together with Raviv (IEEE Trans Inf Theory 62(4):1605–1615, 2016), proved that Gabidulin codes cannot be efficiently list decoded for any radius τ, providing that τ is large enough. Also, they proved that there are infinitely many choices of the parameters for which Gabidulin codes cannot be efficiently list decoded at all. Subsequently, in Trombetti and Zullo (IEEE Trans Inf Theory 66(9):5379–5386, 2020) these results have been extended to the family of generalized Gabidulin codes and to further family of MRD-codes. In this paper, we provide bounds on the list size of rank-metric codes containing generalized Gabidulin codes in order to determine whether or not a polynomial-time list decoding algorithm exists. We detect several families of rank-metric codes containing a generalized Gabidulin code as subcode which cannot be efficiently list decoded for any radius large enough and families of rank-metric codes which cannot be efficiently list decoded. These results suggest that rank-metric codes which are Fqm-linear or that contains a (power of) generalized Gabidulin code cannot be efficiently list decoded for large values of the radius
Extending two families of maximum rank distance codes
No full textIn this paper, we properly extend the family of rank-metric codes recently found by Longobardi and Zanella (2021) and by Longobardi, Marino, Trombetti and Zhou (2021). These codes are Fqjavax.xml.bind.JAXBElement@5067231d-linear of dimension 2 in the space of linearized polynomials over Fqjavax.xml.bind.JAXBElement@26e44682, where t is any integer greater than 2, and we prove that they are maximum rank distance codes. For t≥5, we determine their equivalence classes and these codes turn out to be inequivalent to any other construction known so far, and hence they are really new
Classifications and constructions of minimum size linear sets on the projective line
No full textThis paper aims to study linear sets of minimum size on the projective line, that is Fq-linear sets of rank k in PG(1,qn) admitting one point of weight one and having size qk−1+1. Examples of these linear sets have been found by Lunardon and the second author (2000) and, more recently, by Jena and Van de Voorde (2021). However, classification results for minimum size linear sets are known only for k≤5. In this paper we provide classification results for minimum size linear sets admitting two points with complementary weights. We construct new examples (not necessarily with complementary weights) and also study the related ΓL(2,qn)-equivalence issue. These results solve an open problem posed by Jena and Van de Voorde. The main tool relies on two results by Bachoc, Serra and Zémor (2017 and 2018) on the linear analogues of Kneser's and Vosper's theorems. We then conclude the paper pointing out a connection between critical pairs and linear sets, obtaining also some classification results for critical pairs
The geometry of one-weight codes in the sum-rank metric
No full textWe provide a geometric characterization of k-dimensional Fq^m-linear sum-rank metric codes as tuples of Fq-subspaces of F{q^m}^k. We then use this characterization to study one-weight codes in the sum-rank metric. This leads us to extend the family of linearized Reed-Solomon codes in order to obtain a doubly-extended version of them. We prove that these codes are still maximum sum-rank distance (MSRD) codes and, when k=2, they are one-weight, as in the Hamming-metric case. We then focus on constant rank-profile codes in the sum-rank metric, which are a special family of one weight-codes, and derive constraints on their parameters with the aid of an associated Hamming-metric code. Furthermore, we introduce the n-simplex codes in the sum-rank metric, which are obtained as the orbit of a Singer subgroup of GL(k,qm). They turn out to be constant rank-profile – and hence one-weight – and generalize the simplex codes in both the Hamming and the rank metric. Finally, we focus on 2-dimensional one-weight codes, deriving constraints on the parameters of those which are also MSRD, and we find a new construction of one-weight MSRD codes when q=2
RODRIGUEZ D, ARSENI A. L’esercizio della professione: i fondamentali riferimenti normativi.
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