933 research outputs found
Non-linear maximum rank distance codes in the cyclic model for the field reduction of finite geometries
In this paper we construct infinite families of non-linear maximum rank
distance codes by using the setting of bilinear forms of a finite vector space.
We also give a geometric description of such codes by using the cyclic model
for the field reduction of finite geometries and we show that these families
contain the non-linear maximum rank distance codes recently provided by
Cossidente, Marino and Pavese.Comment: submitted; 22 page
(B)-Geometries and flocks of hyperbolic quadrics
AbstractWe give a characteristic-free proof of the classification theorem for flocks of hyperbolic quadrics of PG(3,q)
Absolute points of correlations of
The sets of the absolute points of (possibly degenerate) polarities of a projective space
are well known. The sets of the absolute points of (possibly degenerate) correlations,
different from polarities, of PG(2, qn), have been completely determined by B.C.
Kestenband in 11 papers from 1990 to 2014, for non-degenerate correlations and
by D’haeseleer and Durante (Electron J Combin 27(2):2–32, 2020) for degenerate
correlations. In this paper, we completely determine the sets of the absolute points
of degenerate correlations, different from degenerate polarities, of a projective space
PG(3, qn). As an application we show that, for q even, some of these sets are related
to the Segre’s (2h +1)-arc of PG(3, 2n) and to the Lüneburg spread of PG(3, 22h+1)
Low dimensional models of the finite split Cayley hexagon
We provide a model of the split Cayley hexagon arising from the Hermitian
surface , thereby yielding a geometric construction of the
Dickson group starting with the unitary group
The Grassmann Space of a Planar Space
AbstractIn this paper we give a characterization of the Grassmann space of a planar space
Clustering of time series via non-parametric tail dependence estimation
We present a procedure for clustering time series according to their tail dependence behaviour as measured via a suitable copula-based tail coefficient, estimated in a non-parametric way. Simulation results about the proposed methodology together with an application to financial data are presented showing the usefulness of the proposed approach
Non-linear MRD codes from cones over exterior sets
By using the notion of -embedding of a (canonical) subgeometry
and of exterior set with respect to the -secant variety
of a subset , , in
the finite projective space , , in this article
we construct a class of non-linear -MRD codes for any . A code of this class, where and is a generator of
, arises from a cone of
with vertex an -dimensional subspace over a
maximum exterior set with respect to . We
prove that the codes introduced in [Cossidente, A., Marino, G., Pavese, F.:
Non-linear maximum rank distance codes. Des. Codes Cryptogr. 79, 597--609
(2016); Durante, N., Siciliano, A.: Non-linear maximum rank distance codes in
the cyclic model for the field reduction of finite geometries. Electron. J.
Comb. (2017); Donati, G., Durante, N.: A generalization of the normal rational
curve in and its associated non-linear MRD codes. Des.
Codes Cryptogr. 86, 1175--1184 (2018)] are appropriate punctured ones of
and solve completely the inequivalence issue for this
class showing that is neither equivalent nor adjointly
equivalent to the non-linear MRD code , , obtained in [Otal, K., \"Ozbudak, F.: Some new
non-additive maximum rank distance codes. Finite Fields and Their Applications
50, 293--303 (2018).]
On the classification of low degree ovoids of
Ovoids of the Klein quadric of have been
studied in the last 40 year, also because of their connection with spreads of
and hence translation planes. Beside the classical example
given by a three dimensional elliptic quadric (corresponding to the regular
spread of ) many other classes of examples are known. First
of all the other examples (beside the elliptic quadric) of ovoids of
give also examples of ovoids of . Another important class of ovoids
of is given by the ones associated to a flock of a three dimensional
quadratic cone. To every ovoid of two bivariate polynomials
and can be associated. In this paper, we classify ovoids
of such that and
, that is
and have "low degree" compared with .Comment: Submitted to Journal of Algebraic Combinatorics. arXiv admin note:
substantial text overlap with arXiv:2203.1468
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