The Poincaré Polynomial of a Linear Code

We introduce the Poincaré polynomial of a linear q-ary code and its relation to the corresponding weight enumerator. The question of whether the Poincaré polynomial is a complete invariant is answered affirmatively for q = 2, 3 and negatively for q ≥ 4. Finally we determine this polynomial for MDS codes and, by means of a recursive formula, for binary Reed-Muller codes

Securing the Downside Up: Client and Care Factors Associated with Outcomes of Secure Residential Youth Care

Although secure residential care has the potential of reducing young people's behavioral problems, it is often difficult to achieve positive outcomes. Research suggests that there are several common success factors of treatment, of which the client's motivation for treatment and the quality of the therapeutic relationship between clients and therapists might be especially relevant and important in the context of secure residential care. The objective of the present study was to explore the association of these potential success factors with secure residential care outcomes. A repeated measures research design was applied in the study, including a group of adolescents in a secure residential care center that was followed up on three measurements in time. Interviews and questionnaires concerning care outcomes in terms of adolescents' behavior change during care were administered to 22 adolescents and 27 group care workers. Outcomes in terms of adolescents' treatment satisfaction were assessed by the use of questionnaires, which were completed by 51 adolescents. Adolescents reported some positive changes in their treatment motivation, but those who were more likely to be motivated at admission were also more likely to deteriorate in treatment motivation from admission to departure. Treatment satisfaction was associated with better treatment motivation at admission and with a positive adolescent-group care worker relationship. The results suggest that outcomes can be improved by a more explicit treatment focus on improving the adolescent's treatment motivation and the quality of the adolescent-care worker relationship during secure residential care

On defining generalized rank weights

This paper investigates the generalized rank weights, with a definition implied by the study of the generalized rank weight enumerator. We study rank metric codes over L, where L is a finite extension of a field K. This is a generalization of the case where K = Fq and L = Fqm of Gabidulin codes to arbitrary characteristic. We show equivalence to previous definitions, in particular the ones by Kurihara-Matsumoto-Uyematsu [12, 13], Oggier-Sboui [16] and Ducoat [6]. As an application of the notion of generalized rank weights, we discuss codes that are degenerate with respect to the rank metric

On defining generalized rank weights

This paper investigates the generalized rank weights, with a definition implied by the study of the generalized rank weight enumerator. We study rank metric codes over L, where L is a finite extension of a field K. This is a generalization of the case where K = Fq and L = Fqm of Gabidulin codes to arbitrary characteristic. We show equivalence to previous definitions, in particular the ones by Kurihara-Matsumoto-Uyematsu [12, 13], Oggier-Sboui [16] and Ducoat [6]. As an application of the notion of generalized rank weights, we discuss codes that are degenerate with respect to the rank metric.</p