Matrix-product constructions of digital nets

Niederreiter, H
Özbudak, Ferruh
We present a new construction of digital nets, and more generally of (d,k,m,s)-systems, over finite fields which is an analog of the matrix-product construction of codes. Examples show that this construction can yield digital nets with better parameters compared to competing constructions.


Curves with many points and configurations of hyperplanes over finite fields
Özbudak, Ferruh (Elsevier BV, 1999-10-01)
We establish a correspondence between a class of Kummer extensions of the rational function field and configurations of hyperplanes in an affine space. Using this correspondence, we obtain explicit curves over finite fields with many rational points. Some of our examples almost attain the Oesterle bound. (C) 1999 Academic Press.
Fibre products of Kummer covers and curves with many points
Özbudak, Ferruh (Springer Science and Business Media LLC, 2007-10-01)
We study the general fibre product of any two Kummer covers of the projective line over finite fields. Under some assumptions, we obtain an involved condition for the existence of rational points in the fibre product over a rational point of the projective line so that we determine the exact number of the rational points. Using this, we construct explicit examples of such fibre products with many rational points. In particular we obtain a record and a new entry for the table (
A minimum distance bound for quasi-nD-cyclic codes
Özbudak, Ferruh (Elsevier BV, 2016-09-01)
We provide a new concatenated structure for multidimensional quasi-cyclic (QnDC) codes over F-q and we give a trace representation for their codewords, which extends the known representations of QC and nD cyclic codes. Based on these results, we obtain a minimum distance bound for QnDC dyclic codes. Since QnDC codes are naturally related to nD convolutional codes, this bound also applies to a special class of 1-generator 2D convolutional codes.
Quantum system structures of quantum spaces and entanglement breaking maps
Dosi, A. A. (IOP Publishing, 2019-07-01)
This paper is devoted to the classification of quantum systems among the quantum spaces. In the normed case we obtain a complete solution to the problem when an operator space turns out to be an operator system. The min and max quantizations of a local order are described in terms of the min and max envelopes of the related state spaces. Finally, we characterize min-max-completely positive maps between Archimedean order unit spaces and investigate entanglement breaking maps in the general setting of quantum...
Codes on fibre products of some Kummer coverings
Özbudak, Ferruh (Elsevier BV, 1999-04-01)
The purpose of this paper is to construct fairly long geometric Goppa codes over F-q with rather good parameters by fibre products of some Kummer coverings, This paper also extends the results of Stepanov [1] and Stepanov and Ozbudak [2]. (C) 1999 Academic Press.
Citation Formats
H. Niederreiter and F. Özbudak, “Matrix-product constructions of digital nets,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 464–479, 2004, Accessed: 00, 2020. [Online]. Available: