Intersection sets, three-character multisets and associated codes

In this article we construct new minimal intersection sets in ${\mathrm{AG}}(r,q^2)$ sporting three intersection numbers with hyperplanes; we then use these sets to obtain linear error correcting codes with few weights, whose weight enumerator we also determine. Furthermore, we provide a new family of three-character multisets in ${\mathrm{PG}}(r,q^2)$ with $r$ even and we also compute their weight distribution.Comment: 17 Pages; revised and corrected result

Intersections of the Hermitian surface with irreducible quadrics in PG(3,q2)PG(3,q^2), qq odd

In $PG(3,q^2)$, with $q$ odd, we determine the possible intersection sizes of a Hermitian surface $\mathcal{H}$ and an irreducible quadric $\mathcal{Q}$ having the same tangent plane $\pi$ at a common point $P\in{\mathcal Q}\cap{\mathcal H}$.Comment: 14 pages; clarified the case q=

Intersections of the Hermitian Surface with irreducible Quadrics in even Characteristic

We determine the possible intersection sizes of a Hermitian surface $\mathcal H$ with an irreducible quadric of ${\mathrm PG}(3,q^2)$ sharing at least a tangent plane at a common non-singular point when $q$ is even.Comment: 20 pages; extensively revised and corrected version. This paper extends the results of arXiv:1307.8386 to the case q eve

Quasi--Hermitian varieties in PG(r,q^2), q even

In this paper a new example of quasi--Hermitian variety \cV in $PG(r,q^2)$, $q$ an odd power of $2$, is provided. In higher-dimensional spaces \cV can be viewed as a generalization of the Buekenhout-Tits unital in the desarguesian projective plane; see \cite{GE2}

tt-Intersection sets in AG(r,q2)AG(r,q^2) and two-character multisets in PG(3,q2)PG(3,q^2)

In this article we construct new minimal intersection sets in $AG(r,q^2)$ with respect to hyperplanes, of size $q^2r-1$ and multiplicity $t$, where $t\in \ q^2r-3-q^(3r-5)/2, q^2r-3+q^(3r-5)/2-q^(3r-3)/2\$, for$r$odd or$t \in \ q^2r-3-q^(3r-4)/2, q^2r-3-q^r-2\$, for$r$even. As a byproduct, for any odd$q$we get a new family of two-character multisets in$PG(3,q^2)$. The essential idea is to investigate some point-sets in$AG(r,q^2)$ satisfying the opposite of the algebraic conditions required in [1] for quasi--Hermitian varieties

On Hermitian varieties in PG(6,q2)\mathrm{PG}(6,q^2)

In this paper we characterize the non-singular Hermitian variety ${\mathcal H}(6,q^2)$ of $\mathrm{PG}(6, q^2)$, $q\neq2$ among the irreducible hypersurfaces of degree $q+1$ in $\mathrm{PG}(6, q^2)$ not containing solids by the number of its points and the existence of a solid $S$ meeting it in $q^4+q^2+1$ points.Comment: 13 pages/revised versio

On regular sets of affine type in finite Desarguesian planes and related codes

In this paper, we consider point sets of finite Desarguesian planes whose multisets of intersection numbers with lines is the same for all but one exceptional parallel class of lines. We call such sets regular of affine type. When the lines of the exceptional parallel class have the same intersection numbers, then we call these sets regular of pointed type. Classical examples are e.g. unitals; a detailed study and constructions of such sets with few intersection numbers is due to Hirschfeld and Sz\H{o}nyi from 1991. We here provide some general construction methods for regular sets and describe a few infinite families. The members of one of these families have the size of a unital and meet affine lines of $\mathrm{PG}(2, q^2)$ in one of $4$ possible intersection numbers, each of them congruent to $1$ modulo $\sqrt{q}$. As a byproduct, we determine the intersection sizes of the Hermitian curve defined over $\mathrm{GF}(q^2)$ with suitable rational curves of degree $\sqrt{q}$ and we obtain $\sqrt{q}$-divisible codes with $5$ non-zero weights. We also determine the weight enumerator of the codes arising from the general constructions modulus some $q$-powers.Comment: 16 pages/revised and improved versio

Accuracy of self-assessment of real-life functioning in schizophrenia

A consensus has not yet been reached regarding the accuracy of people with schizophrenia in self-reporting their real-life functioning. In a large (n=618) cohort of stable, community-dwelling schizophrenia patients we sought to: (1) examine the concordance of patients' reports of their real-life functioning with the reports of their key caregiver; (2) identify which patient characteristics are associated to the differences between patients and informants. Patient-caregiver concordance of the ratings in three Specific Level of Functioning Scale (SLOF) domains (interpersonal relationships, everyday life skills, work skills) was evaluated with matched-pair t tests, the Lin's concordance correlation, Somers' D, and Bland-Altman plots with limits of agreement (LOA). Predictors of the patient-caregiver differences in SLOF ratings were assessed with a linear regression with multivariable fractional polynomials. Patients' self-evaluation of functioning was higher than caregivers' in all the evaluated domains of the SLOF and 17.6% of the patients exceeded the LOA, thus providing a self-evaluation discordant from their key caregivers. The strongest predictors of patient-caregiver discrepancies were caregivers' ratings in each SLOF domain. In clinically stable outpatients with a moderate degree of functional impairment, self-evaluation with the SLOF scale can become a useful, informative and reliable clinical tool to design a tailored rehabilitation program