26 citations · 96 across the 41 of their papers we have counts for
18 papers · 1 filter
Semifields in prime dimensions and counterexamples to Kaplansky's conjecture
Gábor P. Nagy, Yue Zhou
In 1975, Kaplansky conjectured that every five-dimensional division algebra over a sufficiently large finite field is a field or a twisted field. We disprove this conjecture. For e…
On a conjecture on the Kasami APN function: reductions, structure theorems, a proof for , and exhaustive verification for
Gábor P. Nagy, Attila Vajda
We study Carlet's cyclic-additive conjecture for the Kasami almost perfect nonlinear (APN) function on , : for the -element set…
Vertex-transitive strongly regular graphs in the switching class of doubly transitive two-graphs
Robert F. Bailey, Gábor P. Nagy, Valentino Smaldore
Let be a permutation group that acts -transitively on the finite set and let be a two-graph whose automorphism group contains . In this paper, we…
On the minimum Hamming distance between vectorial Boolean and affine functions
Gabor P. Nagy
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 u…
Switching equivalence of strongly regular polar graphs
Gábor P. Nagy, Valentino Smaldore
We prove the switching equivalence of the strongly regular polar graphs , , and plus an isolated vertex by giving an analytic descrip…
Simplicity conditions for binary orthogonal arrays
Claude Carlet, Rebeka Kiss, Gábor P. Nagy
It is known that correlation-immune (CI) Boolean functions used in the framework of side-channel attacks need to have low Hamming weights. The supports of CI functions are (equival…
On the nonexistence of certain orthogonal arrays of strength four
Rebeka Kiss, Gábor P. Nagy
We show that no orthogonal arrays exist with and . This solves an open problem of the NSUCRYPTO Olympiad 2018. Our result allows us to determine the…
Embeddings of Ree unitals in a projective plane over a field
Gábor P. Nagy
We show that the Ree unital has an embedding in a projective plane over a field if and only if and is a subfield of . In this case, the…
New Steiner systems from old ones by paramodifications
Dávid Mezőfi, Gábor P. Nagy
Techniques of producing new combinatorial structures from old ones are commonly called trades. The switching principle applies for a broad class of designs: it is a local transform…
On the geometry of full points of abstract unitals
Dávid Mezőfi, Gábor P. Nagy
The concept of full points of abstract unitals has been introduced by Korchmáros, Siciliano and Szőnyi as a tool for the study of projective embeddings of abstract unitals. In this…
Light dual multinets of order six in the projective plane
Norbert Bogya, Gábor P. Nagy
The aim of this paper is twofold: First we classify all abstract light dual multinets of order which have a unique line of length at least two. Then we classify the weak projec…
Inherited conics in Hall planes
Aart Blokhuis, István Kovács, Gábor P. Nagy +1
The existence of ovals and hyperovals is an old question in the theory of non-Desarguesian planes. The aim of this paper is to describe when a conic of remains an a…
Hemisystems of the Hermitian Surface
Gábor Korchmáros, Gábor P. Nagy, Pietro Speziali
We present a new method for the study of hemisystems of the Hermitian surface of . The basic idea is to represent generator-sets of by me…
Group-labeled light dual multinets in the projective plane (with Appendix)
Gábor Korchmáros, Gábor P. Nagy
In this paper we investigate light dual multinets labeled by a finite group in the projective plane defined over a field . We present two classes of…
Classification of k-nets
G. Korchmáros, G. P. Nagy
A finite \emph{-net} of order is an incidence structure consisting of pairwise disjoint classes of lines, each of size , such that every point incident with two…
Binary Fields on Limited Systems
Valentino Lanzone, Gábor P. Nagy
The intrinsic structure of binary fields poses a challenging complexity problem from both hardware and software point of view. Motivated by applications to modern cryptography, we…
Linear groups as right multiplication groups of quasifields
Gábor P. Nagy
For quasifields, the concept of parastrophy is slightly weaker than isotopy. Parastrophic quasifields yield isomorphic translation planes but not conversely. We investigate the rig…
Direct construction of code loops
Gabor P. Nagy
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…