Related papers: On the linear structures of Balanced functions and…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
Using semi-tensor product of matrices, the structures of several kinds of symmetric games are investigated via the linear representation of symmetric group in the structure vector of games as its representation space. First of all, the…
(NxN)-matrix is called additive when its elements are pair-wise sums of N real numbers. For a quadratic binary functional with an additive connection matrix we succeeded in finding the global minimum expressing it through external…
We examine so-called rank function equations and their solutions consisting of non-nilpotent matrices. Secondly, we present some geometrical properties of the set of solutions to certain rank function equations in the nilpotent case.
Functions with low differential uniformity have relevant applications in cryptography. Recently, functions with low $c$-differential uniformity attracted lots of attention. In particular, so-called APcN and PcN functions (generalization of…
We study a new method of constructing Boolean bent functions from cyclotomic mappings. Three generic constructions are obtained by considering different branch functions such as Dillon functions, Niho functions and Kasami functions over…
In this paper, we consider the problem of finding perfectly balanced Boolean functions with high non-linearity values. Such functions have extensive applications in domains such as cryptography and error-correcting coding theory. We provide…
We give improved bounds for our theorem in [GW09], which shows that a system of linear forms on $\mathbb{F}_p^n$ with squares that are linearly independent has the expected number of solutions in any linearly uniform subset of…
We investigate classification results for general quadratic functions on torsion abelian groups. Unlike the previously studied situations, general quadratic functions are allowed to be inhomogeneous or degenerate. We study the discriminant…
Our main result is a generalized Dillon-type theorem, giving graph-theoretic conditions which guarantee that a $p$-ary function in an even number of variables is bent, for $p$ a prime number greater than 2. The key condition is that the…
A fundamental problem in quantum physics is to encode functions that are completely anti-symmetric under permutations of identical particles. The Barron space consists of high-dimensional functions that can be parameterized by infinite…
The generic structure of 4-point functions of fields residing in indecomposable representations of arbitrary rank is given. The presented algorithm is illustrated with some non-trivial examples and permutation symmetries are exploited to…
We propose a representation of boolean bent functions by bent rectangles, that is, by special matrices with restrictions on rows and columns. Using this representation, we exhibit new classes of bent functions, give an algorithm to…
The dynamics of Boolean networks (BN) with quenched disorder and thermal noise is studied via the generating functional method. A general formulation, suitable for BN with any distribution of Boolean functions, is developed. It provides…
A geometric structure (FAP-structure), having both absolute parallelism and Finsler properties, is constructed. The building blocks of this structures are assumed to be functions of position and direction. A non-linear connection emerges…
Relu Fully Connected Networks are ubiquitous but uninterpretable because they fit piecewise linear functions emerging from multi-layered structures and complex interactions of model weights. This paper takes a novel approach to piecewise…
Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…
Complex dynamics deals with the iteration of holomorphic functions. As is well- known, the first functions to be studied which gave non-trivial dynamics were quadratic polynomials, which produced beautiful computer generated pictures of…
A method of reducing general quaternion functions of first degree, i.e., linear quaternion functions, to quaternary canonical form is given. Linear quaternion functions, once reduced to canonical form, can be maintained in this form under…
Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…