Related papers: Cross-correlation properties of cyclotomic sequenc…
The autocorrelation and the linear complexity of a key stream sequence in a stream cipher are important cryptographic properties. Many sequences with these good properties have interleaved structure, three classes of binary sequences of…
In this paper we investigate a spectra of the Laplacian matrix of cyclic groups using the properties of their characteristic polynomials. We have proved several assertions about the relationship between the spectra of different groups.
We analyze the connection between the autocorrelation of a binary sequence and its run structure given by the run length encoding. We show that both the periodic and the aperiodic autocorrelation of a binary sequence can be formulated in…
The time-ordered multilayer integrals have long been cited as major challenges in the analytical study of cosmological correlators and wavefunction coefficients. The recently proposed family tree decomposition technique solved these time…
The investigation of the static and dynamic structural properties of colloidal systems relies on techniques capable of atomic resolution in real space and femtosecond resolution in time. Recently, the cross-correlation function (CCF)…
The scattering matrix was measured for microwave cavities with two antennas. It was analyzed in the regime of overlapping resonances. The theoretical description in terms of a statistical scattering matrix and the rescaled Breit-Wigner…
We introduce group crosscoders, an extension of crosscoders that systematically discover and analyse symmetrical features in neural networks. While neural networks often develop equivariant representations without explicit architectural…
Short cycles connectivity is a generalization of ordinary connectivity. Instead by a path (sequence of edges), two vertices have to be connected by a sequence of short cycles, in which two adjacent cycles have at least one common vertex. If…
Connecting curves have been shown to organize the rotational structure of strange attractors in three-dimensional dynamical systems. We extend the description of connecting curves and their properties to higher dimensions within the special…
We define a family of four-point invariants for Shilov boundaries of bounded symmetric domains of tube type, which generalizes the classical four-point cross ratio on the unit circle. This generalization, which is based on a similar…
This paper presents a class of random orthogonal sequences associated with the number theoretic Hilbert transform. We present a constructive procedure for finding the random sequences for different modulus values. These random sequences…
Families of codes such as group codes, constacyclic and skew cyclic codes, some of which independently suggested in the literature, turn out to be special instances of the general family of crossed product codes. Hamming-metric is a main…
In this work, we study cyclic codes that have generators as Fibonacci polynomials over finite fields. We show that these cyclic codes in most cases produce families of maximum distance separable and optimal codes with interesting…
Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…
Cross phenomena, representing responses of a system to external stimuli, are ubiquitous from quantum to macro scale. The Onsager theorem is often used to describe them, stating that the coefficient matrix of cross phenomena connecting the…
Binary sequences with minimal autocorrelations have applications in communication engineering, mathematics and computer science. In statistical physics they appear as groundstates of the Bernasconi model. Finding these sequences is a…
(Strong) circular external difference families (which we denote as CEDFs and SCEDFs) can be used to construct nonmalleable threshold schemes. They are a variation of (strong) external difference families, which have been extensively studied…
Two approaches to studying the correlation functions of the binary Markov sequences are considered. The first of them is based on the study of probability of occurring different ''words'' in the sequence. The other one uses recurrence…
We use cyclotomy to design new classes of permutation polynomials over finite fields. This allows us to generate many classes of permutation polynomials in an algorithmic way. Many of them are permutation polynomials of large indices.
We show that graphs, networks and other related discrete model systems carry a natural supersymmetric structure, which, apart from its conceptual importance as to possible physical applications, allows to derive a series of spectral…