Maximum scattered linear sets and MRD-codes

The rank of a scattered -linear set of , rn even, is at most rn / 2 as it was proved by Blokhuis and Lavrauw. Existence results and explicit constructions were given for infinitely many values of r, n, q (rn even) for scattered -linear sets of rank rn / 2. In this paper, we prove that the bound rn / 2 is sharp also in the remaining open cases. Recently Sheekey proved that scattered -linear sets of of maximum rank n yield -linear MRD-codes with dimension 2n and minimum distance . We generalize this result and show that scattered -linear sets of of maximum rank rn / 2 yield -linear MRD-codes with dimension rn and minimum distance n - 1

New maximum scattered linear sets of the projective line

In [2] and [18] are presented the first two families of maximum scattered Fq-linear sets of the projective line PG(1,qn). More recently in [22] and in [5], new examples of maximum scattered Fq-subspaces of V(2,qn) have been constructed, but the equivalence problem of the corresponding linear sets is left open. Here we show that the Fq-linear sets presented in [22] and in [5], for n=6,8, are new. Also, for q odd, q≡±1,0(mod5), we present new examples of maximum scattered Fq-linear sets in PG(1,q6), arising from trinomial polynomials, which define new Fq-linear MRD-codes of Fq6×6 with dimension 12, minimum distance 5 and left idealiser isomorphic to Fqjavax.xml.bind.JAXBElement@52ca3f68

Small complete caps in PG(4n + 1, q)

In this paper we prove the existence of a complete cap of (Formula presented.) of size (Formula presented.), for each prime power (Formula presented.). It is obtained by projecting two disjoint Veronese varieties of (Formula presented.) from a suitable (Formula presented.) -dimensional projective space. This shows that the trivial lower bound for the size of the smallest complete cap of (Formula presented.) is essentially sharp

Generalising the Scattered Property of Subspaces

Let V be an r-dimensional Fqn-vector space. We call an Fq-subspace U of V h-scattered if U meets the h-dimensional Fqn-subspaces of V in Fq-subspaces of dimension at most h. In 2000 Blokhuis and Lavrauw proved that dimFqU ≤ rn/2 when U is 1-scattered. Sub-spaces attaining this bound have been investigated intensively because of their relations with projective two-weight codes and strongly regular graphs. MRD-codes with a maximum idealiser have also been linked to rn/2-dimensional 1-scattered subspaces and to n-dimensional (r − 1)-scattered subspaces. In this paper we prove the upper bound rn/(h + 1) for the dimension of h-scattered subspaces, h > 1, and construct examples with this dimension. We study their intersection numbers with hyperplanes, introduce a duality relation among them, and study the equivalence problem of the corresponding linear sets

Macroprudential stress-testing practices of central banks in Central and Southeastern Europe: comparison and challenges ahead

This paper reviews and compares stress-testing practices of central banks in Central and Southeastern Europe (CSEECBs) and outlines challenges in the area of stress testing going forward. The authors, focusing their comparison on CSEECBs, construct the baseline and stress scenarios, map macroeconomic scenarios and microeconomic factors to risk factors, calculate risk exposures to different risk indicators, and estimate outcome indicators to inform macroprudential policy. The main challenges going forward concern data reliability, consideration of quantitative microprudential indicators, incorporation of feedback effects in stress tests, institutionalization of macroprudential policy responses to alarming stress-test results, and information exchange for better cross-border supervision.Web of Science48414311

Comparing different methods for the estimation of interbank intraday yield curves

Gefördert im Rahmen des Projekts DEA