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Gabor P. Nagy

Publications and source records attributed to Gabor P. Nagy.

9 recordsLinked to original sources
arXiv2025

On the minimum Hamming distance between vectorial Boolean and affine functions

In this paper, we study the Hamming distance between vectorial Boolean functions and affine functions. This parameter is known to be related to the non-linearity and differential uniformity of vectorial functions, while the calculation of it is in general difficult. In 2017, Liu, Mesnager and Chen conjectured an upper bound for this metric. We prove this bound for two classes of vectorial bent functions, obtained from finite quasigroups in characteristic two, and we improve the known bounds for two classes of monomial functions of differential uniformity two or four. For many of the known APN functions of dimension at most nine, we compute the exact distance to affine functions.

math.CO↗
arXiv2024

An extension formula for right Bol loops arising from Bol reflections

We study a new extension formula for right Bol loops. We prove the necessary or sufficient conditions for the extension to be right Bol. We describe the most important invariants: right multiplication group, nuclei, and center. We show that the core is an involutory quandle which is the disjoint union of two isomorphic involutory quandles. We also derive further results on the structure group of the core of the extension.

math.GR↗
arXiv2011

Some computational results on small 3-nets embedded in a projective plane over a field

In this paper, we investigate dual 3-nets realizing the groups $C_3 \times C_3$, $C_2 \times C_4$, $\Alt_4$ and that can be embedded in a projective plane $PG(2,\mathbb K)$, where $\mathbb K$ is an algebraically closed field. We give a symbolically verifiable computational proof that every dual 3-net realizing the groups $C_3 \times C_3$ and $C_2 \times C_4$ is algebraic, namely, that its points lie on a plane cubic. Moreover, we present two computer programs whose calculations show that the group $\Alt_4$ cannot be realized if the characteristic of $\mathbb K$ is zero.

math.GR↗
arXiv2007

A class of finite simple Bol loops of exponent 2

In this paper we give an infinite class of finite simple right Bol loops of exponent 2. The right multiplication group of these loops is an extension of an elementary Abelian 2-group by $S_5$. The construction uses the description of the structure of such loops given by M. Aschbacher. These results answer some questions of M. Aschbacher.

math.GR↗
arXiv2007

A class of simple proper Bol loops

The existence of finite simple non-Moufang Bol loops was considered as one of the main open problems in the theory of loops and quasigroups. In this paper, we present a class of proper simple Bol loops. This class also contains finite and new infinite simple proper Bol loops.

math.GR↗
arXiv2004

Direct construction of code loops

Code loops were introduced by R. L. Griess. R.L. Griess and T. Hsu gave methods to construct the corresponding code loop from any given doubly even binary code; both these methods used some kind of induction. In this paper, we present a global construction of the loop, where we apply the correspondance between the concepts of Moufang loops and groups with triality.

math.CO↗
arXiv2004

Collineation groups of the smallest Bol 3-nets

Some associativity properties of a loop can be interpreted as certain closure configuration of the corresponding 3-net. It was known that the smallest non-associative loops with the so called left Bol property have order 8. In this paper, we determine the direction preserving collineation groups of the 3-nets belonging to these smallest Bol loops. For that, we prove some new results concerning collineations of 3-nets and autotopisms of loops.

math.GR↗
arXiv2004

Group invariants of certain Burn loop classes

In this paper, we determine the collineation groups generated by the Bol reflections, the core, the automorphism groups and the full direction preserving collineation groups of the loops $B_{4n}$ and $C_{4n}$ given by R.P. Burn. We also prove some lemmas and use new methods in order to simplify the calculations in these groups.

math.GR↗