6 papers
The paired construction for Boolean functions on the slice
Michael Kiermaier, Jonathan Mannaert, Alfred Wassermann
Let be a finite set of size . We consider real functions on the "slice" , which are also known as functions in the Johnson scheme. For $I \subseteq J \subseteq…
The degree of functions in the Johnson and q-Johnson schemes
Michael Kiermaier, Jonathan Mannaert, Alfred Wassermann
In 1982, Cameron and Liebler investigated certain "special sets of lines" in PG(3,q), and gave several equivalent characterizations. Due to their interesting geometric and algebrai…
Designs in finite classical polar spaces
Michael Kiermaier, Kai-Uwe Schmidt, Alfred Wassermann
Combinatorial designs have been studied for nearly 200 years. Fifty years ago, Cameron, Delsarte, and Ray-Chaudhury started investigating their q-analogs, also known as subspace de…
Steiner 3-designs as extensions
Michael Kiermaier, Vedran KrÄadinac, Alfred Wassermann
In this article, we construct a Steiner system with the parameters , settling one of the smallest open parameter sets of Steiner -designs. Furthermore, we establish t…
Varieties of Nodal surfaces, coding theory and Discriminants of cubic hypersurfaces. Part 1: Generalities and nodal K3 surfaces. Part 2: Cubic Hypersurfaces, associated discriminants. Part 3: Nodal quintics. Part 4: Nodal sextics
Fabrizio Catanese, in collaboration with Yonghwa Cho, Stephen Coughlan +4
We attach two binary codes to a projective nodal surface (the strict code K and, for even degree d, the extended code K' ) to investigate the `Nodal Severi varieties F(d, n) of nod…
Some new Steiner designs
Michael Kiermaier, Vedran KrÄadinac, Vladimir D. Tonchev +2
The Kramer-Mesner method for constructing designs with a prescribed automorphism group has proven effective many times. In the special case of Steiner designs, the task reduces…