Related papers: On APN functions and their derivatives
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 the paper, by induction, the Fa\`a di Bruno formula, and some techniques in the theory of complex functions, the author finds explicit formulas for higher order derivatives of the tangent and cotangent functions as well as powers of the…
The weight enumerators (quant-ph/9610040) of a quantum code are quite powerful tools for exploring its structure. As the weight enumerators are quadratic invariants of the code, this suggests the consideration of higher-degree polynomial…
Two-to-one ($2$-to-$1$) mappings over finite fields play an important role in symmetric cryptography. In particular they allow to design APN functions, bent functions and semi-bent functions. In this paper we provide a systematic study of…
D. Leviatan has investigated the behavior of the higher order derivatives of approximation polynomials of the differentiable function $f$ on $[-1,1]$. Especially, when $P_n$ is the best approximation of $f$, he estimates the differences…
We study the quantum query complexity of the Boolean hidden shift problem. Given oracle access to f(x+s) for a known Boolean function f, the task is to determine the n-bit string s. The quantum query complexity of this problem depends…
In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…
This work studies the design of neural networks that can process the weights or gradients of other neural networks, which we refer to as neural functional networks (NFNs). Despite a wide range of potential applications, including learned…
In this work we cast the problem of binary classification in terms of estimating a partition on Bernoulli data. When the explanatory variables are all categorical, the problem can be modelled using the language of boolean functions. We…
We associate a weight function to pairs consisting of a smooth and proper variety X over a complete discretely valued field and a differential form on X of maximal degree. This weight function is a real-valued function on the…
Boolean functions with good cryptographic criteria when restricted to the set of vectors with constant Hamming weight play an important role in the recent FLIP stream cipher. In this paper, we propose a large class of weightwise perfectly…
We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the…
This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…
Inspired by prior work of Bruinier and Ono and Mertens and Rolen, we study class polynomials for non-holomorphic modular functions arising from modular forms of negative weight. In particular, we give general conditions for the…
In this letter, we give a characterization for a generic construction of bent functions. This characterization enables us to obtain another efficient construction of bent functions and to give a positive answer on a problem of bent…
We prove a connection between Schmidt-rank and weight of quadratic forms. This provides a new tool for the classification of graph states based on entanglement. Our main tool arises from a reformulation of previously known results…
We give the cumulative distribution functions, the expected values, and the moments of weighted lattice polynomials when regarded as real functions of independent random variables. Since weighted lattice polynomial functions include…
For a family of polynomials in two continuous variables, orthogonal with respect to a weight function, we prove, under suitable conditions, the equivalence of the following properties: the matrix Pearson equation of the weight, the second…
Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…
We describe bivariate polynomial sequences orthogonal to a symmetric weight function in terms of several bivariate polynomial sequences orthogonal with respect to Christoffel transformations of the initial weight under a quadratic…