Hermitian codes from higher degree places

Matthews and Michel investigated the minimum distances in certain algebraic-geometry codes arising from a higher degree place $P$. In terms of the Weierstrass gap sequence at $P$, they proved a bound that gives an improvement on the designed minimum distance. In this paper, we consider those of such codes which are constructed from the Hermitian function field. We determine the Weierstrass gap sequence $G(P)$ where $P$ is a degree 3 place, and compute the Matthews and Michel bound with the corresponding improvement. We show more improvements using a different approach based on geometry. We also compare our results with the true values of the minimum distances of Hermitian 1-point codes, as well as with estimates due Xing and Chen

Group-labeled light dual multinets in the projective plane (with Appendix)

In this paper we investigate light dual multinets labeled by a finite group in the projective plane $PG(2,\mathbb{K})$ defined over a field $\mathbb{K}$. We present two classes of new examples. Moreover, under some conditions on the characteristic $\mathbb{K}$, we classify group-labeled light dual multinets with lines of length least $9$

3-nets realizing a diassociative loop in a projective plane

A \textit{$3$-net} of order $n$ is a finite incidence structure consisting of points and three pairwise disjoint classes of lines, each of size $n$, such that every point incident with two lines from distinct classes is incident with exactly one line from each of the three classes. The current interest around $3$-nets (embedded) in a projective plane $PG(2,K)$, defined over a field $K$ of characteristic $p$, arose from algebraic geometry. It is not difficult to find $3$-nets in $PG(2,K)$ as far as $0<p\le n$. However, only a few infinite families of $3$-nets in $PG(2,K)$ are known to exist whenever $p=0$, or $p>n$. Under this condition, the known families are characterized as the only $3$-nets in $PG(2,K)$ which can be coordinatized by a group. In this paper we deal with $3$-nets in $PG(2,K)$ which can be coordinatized by a diassociative loop $G$ but not by a group. We prove two structural theorems on $G$. As a corollary, if $G$ is commutative then every non-trivial element of $G$ has the same order, and $G$ has exponent $2$ or $3$. We also discuss the existence problem for such $3$-nets

Mind the Gap – International Comparison of Cyclical Adjustment of the Budget

Cyclically adjusted budget balance (CAB) is a widely cited and widely used concept in the evaluation of fiscal situations. The key idea behind it involves the identification of potential levels of economic variables. There are two recently used methods: the aggregate approach and the unconstrained disaggregate approach. In this paper we apply them on USA, Japan and 25 EU member countries to demonstrate that both approaches could be the source of considerable bias. While the aggregate approach cannot cope with different shocks, the unconstrained disaggregate method involves systematic bias and do not contain theoretical consideration. In order to avoid these distortions we present an alternative framework, which is able to incorporate the advantages of both approaches. Combining arbitrary output gap and constrained multivariate HP filter induces theoretically motivated disaggregation where we also exploit the implication of production function parameterisation. We found that the price effect resulting from the composition effect of different deflators could play an important role in evaluation of the fiscal position. To display the importance of composition effect we analyse the cyclical components of Finnish, Hungarian and Italian budget balances more in detail.cyclically adjusted budget deficit, price gap, business cycles, constrained multivariate HP filter

The Role of General Government in Hungary

The objective of this study is to present the changes in the general government’s role in the distribution and generation of income and in the functions of the state. The period under study is 1991-1997, with an emphasis on the fiscal adjustment which occurred during the years 1995-1996. In relation to this, a separate chapter addresses international experiences in fiscal consolidation and its theoretical aspects. In the period under study, the general government had a certain stabilizing impact. Up to 1993, overspending by the government retarded economic decline and following the commencement of economic growth the adjustment program which became necessary owing to the unsustainability of the external and internal equilibrium put the brakes on growth in the short term. Based on international experience, the most important factor for success is to be sought in the structure of the adjustment. This study concentrates on the presentation of structural changes, and particularly the structure of primary expenditures and revenues, even though its point of departure was the changes in the level of total expenditures and revenues of the general government. Between 1990 and 1997, the volume of the primary levels declined by nearly one quarter and the rearrangements which were effected within this were even more significant. It can be established that the decline was most vigorous on the expenditures side, in the case of expenditures on wages and transfers (particularly with respect to households). According to international experience, the savings achieved precisely in this area can be a guarantee for the lasting success of fiscal adjustment. However, the fiscal retrenchment of 1995-1996 in Hungary does not present us with a clear picture. Personal income tax was increased, there were tax increases of a one-off nature and cuts in public investment, too. This kind of measures were identified as less successful ones by international studies. According to statistics using the prime cost approach, the role of the public sector in income generation declined, as wage costs declined. Were it possible to take quality criteria into account when specifying performance, the picture would be different. According to international experience, some public sectors do not contribute to income generation even at prime cost, and in these areas it is possible to reduce spending without suffering any deterioration in performance. A counterexample can be provided by the tax administration, where a very close correlation can be demonstrated between wages and efficiency. The impact of the Hungarian measures, particularly with respect to changes in the number of persons employed, cannot be evaluated negatively in this respect. In addition to an institutional approach to general government, it is also important to take functional aspects into account - that is to say, it is necessary to the fiscal transparency to demonstrate quasi-fiscal activities performed outside the general government. (This study does not undertake to do so.)

Light dual multinets of order six in the projective plane

The aim of this paper is twofold: First we classify all abstract light dual multinets of order $6$ which have a unique line of length at least two. Then we classify the weak projective embeddings of these objects in projective planes over fields of characteristic zero. For the latter we present a computational algebraic method for the study of weak projective embeddings of finite point-line incidence structures

On the geometry of full points of abstract unitals

The concept of full points of abstract unitals has been introduced by Korchm\'aros, Siciliano and Sz\H{o}nyi as a tool for the study of projective embeddings of abstract unitals. In this paper we give a more detailed description of the combinatorial and geometric structure of the sets of full points in abstract unitals of finite order