Related papers: Vectorial Resilient $PC(l)$ of Order $k$ Boolean F…
Boolean functions are mathematical objects with numerous applications in domains like coding theory, cryptography, and telecommunications. Finding Boolean functions with specific properties is a complex combinatorial optimization problem…
Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…
Algebraic immunity has been proposed as an important property of Boolean functions. To resist algebraic attack, a Boolean function should possess high algebraic immunity. It is well known now that the algebraic immunity of an $n$-variable…
We consider rate R = k/n causal linear codes that map a sequence of k-dimensional binary vectors {b_t} to a sequence of n-dimensional binary vectors {c_t}, such that each c_t is a function of {b_1,b_2,...,b_t}. Such a code is called anytime…
We show an equivalence between 1-query quantum algorithms and representations by degree-2 polynomials. Namely, a partial Boolean function $f$ is computable by a 1-query quantum algorithm with error bounded by $\epsilon<1/2$ iff $f$ can be…
Most modern block ciphers are built using components whose cryptographic strength is evaluated in terms of their resistance to attacks on the whole cipher. In particular, differential properties of vectorial Boolean functions are studied…
Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions can be designed using algebraic constructions or…
In this paper, we introduce strongly regular generalized partial geometries of grade $r$, which generalise partial geometries and strongly regular $(\alpha,\beta)$-geometries. By the properties of quadrics in PG$(2,q)$ and PG$(3,q)$, we…
This paper proposes an algorithm for deciding consistency of systems of Boolean equations in several variables with co-efficients in the two element Boolean algebra $B_{0}=\{0,1\}$ and find all satisfying assignments. The algorithm is based…
The rapid progression in wireless communication technologies, especially in multicarrier code-division multiple access (MC-CDMA), there is a need of advanced code construction methods. Traditional approaches, mainly based on generalized…
NK-Kauffman networks {\cal L}^N_K are a subset of the Boolean functions on N Boolean variables to themselves, \Lambda_N = {\xi: \IZ_2^N \to \IZ_2^N}. To each NK-Kauffman network it is possible to assign a unique Boolean function on N…
Physical Unclonable Functions can be used for secure key generation in cryptographic applications. It is explained how methods from coding theory must be applied in order to ensure reliable key regeneration. Based on previous work, we show…
In this paper, based on the relationship between logic functions and quantum error correcting codes(QECCs), we unify the construction of QECCs via graphs, projectors and logic functions. A construction of QECCs over a prime field GF(p) is…
Principal component analysis (PCA) is a powerful tool for dimensionality reduction. Unfortunately, it is sensitive to outliers, so that various robust PCA variants were proposed in the literature. Among them the so-called rotational…
Time- and state-discrete dynamical systems are frequently used to model molecular networks. This paper provides a collection of mathematical and computational tools for the study of robustness in Boolean network models. The focus is on…
We propose a conservative algorithm to test the geometrical validity of simplicial (triangles, tetrahedra), tensor product (quadrilaterals, hexahedra), and mixed (prisms) elements of arbitrary polynomial order as they deform over a…
We introduce new yet easily accessible codes for elements of $GL_r(A)$ with $A$ the adelic ring of a (dimension one) function field over a finite field. They are linear codes, and coincide with classical algebraic geometry codes when $r=1$.…
Boolean functions with few-valued spectra have wide applications in cryptography, coding theory, sequence designs, etc. In this paper, we further study the parametric construction approach to obtain balanced Boolean functions using…
For $S \subseteq \{0,1\}^n$ a Boolean function $f \colon S \to \{-1,1\}$ is a polynomial threshold function (PTF) of degree $d$ and weight $W$ if there is a polynomial $p$ with integer coefficients of degree $d$ and with sum of absolute…
A new construction for constant weight codes is presented. The codes are constructed from $k$-dimensional subspaces of the vector space $\F_q^n$. These subspaces form a constant dimension code in the Grassmannian space $\cG_q(n,k)$. Some of…