Related papers: Sequences with high nonlinear complexity

We investigate the $k$-error linear complexity of $p^2$-periodic binary sequences defined from the polynomial quotients (including the well-studied Fermat quotients), which is defined by $$ q_{p,w}(u)\equiv \frac{u^w-u^{wp}}{p} \bmod p ~…

The article determines the asymptotic shape of the extremal clusters in stationary regularly varying random fields. To deduce this result, we present a general framework for the Poisson approximation of point processes on Polish spaces…

We study systems of parameters over finite fields from a probabilistic perspective, and use this to give the first effective Noether normalization result over a finite field. Our central technique is an adaptation of Poonen's closed point…

Maximum-length sequences (m-sequences for short) over finite fields are generated by linear feedback shift registers with primitive characteristic polynomials. These sequences have nice mathematical structures and good randomness properties…

We examine a generalization of the binomial distribution associated with a strictly increasing sequence of numbers and we prove its Poisson-like limit. Such generalizations might be found in quantum optics with imperfect detection. We…

The cohomology of the degree-$n$ general linear group over a finite field of characteristic $p$, with coefficients also in characteristic $p$, remains poorly understood. For example, the lowest degree previously known to contain nontrivial…

In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.

This article offers a comprehensive treatment of polynomial functional regression, culminating in the establishment of a novel finite sample bound. This bound encompasses various aspects, including general smoothness conditions, capacity…

In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…

We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…

This paper investigates the synchronization problems for general high-dimensional linear networks over finite fields. By using the technique of linear transformations and invariant subspaces for linear spaces over finite fields, several…

First, we study the linear equations in general. Second, we focus our attention in periodic sequences over finite fields and de Bruijn directed graph.

This paper studies the complexity of languages of finite words using automata theory. To go beyond the class of regular languages, we consider infinite automata and the notion of state complexity defined by Karp. Motivated by the seminal…

It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…

We give an improved polynomial bound on the complexity of the equation solvability problem, or more generally, of finding the value sets of polynomials over finite nilpotent rings. Our proof depends on a result in additive combinatorics,…

This note introduces a class of nonlinear Neumann problems on balls expanding with the radii tending towards infinity. Performing singular perturbation arguments, we establish the corresponding concentration phenomenon and refined…

We establish the density of the partial regularity result in the class of continuous viscosity solutions. Given a fully nonlinear equation, we prove the existence of a sequence entitled to the partial regularity result, approximating its…

We examine some properties of pseudo-multiplications, which are a special kind of associative binary relations defined on $\bar{\mathbb{R}}_+ \times \bar{\mathbb{R}}_+$.

We provide a monotone non increasing sequence of upper bounds $f^H_k$ ($k\ge 1$) converging to the global minimum of a polynomial $f$ on simple sets like the unit hypercube. The novelty with respect to the converging sequence of upper…

This paper examines the randomness of d-sequences, which are decimal sequences to an arbitrary base. Our motivation is to check their suitability for application to cryptography, spread-spectrum systems and use as pseudorandom sequence.