Related papers: Autocorrelation-Run Formula for Binary Sequences
We suggest to construct infinite stochastic binary sequences by associating one of the two symbols of the sequence with the renewal times of an underlying renewal process. Focusing on stationary binary sequences corresponding to delayed…
We study the pseudorandomness of automatic sequences in terms of well-distribution and correlation measure of order 2. We detect non-random behavior which can be derived either from the functional equations satisfied by their generating…
Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in…
We give recurrences, generating functions and explicit exact expressions for the enumeration of fundamental quantities involving runs in binary strings. We first focus on enumerations concerning runs of ones, and we then analyse the same…
Nonlinear complexity is an important measure for assessing the randomness of sequences. In this paper we investigate how circular shifts affect the nonlinear complexities of finite-length binary sequences and then reveal a more explicit…
The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order…
The randomness rate of an infinite binary sequence is characterized by the sequence of ratios between the Kolmogorov complexity and the length of the initial segments of the sequence. It is known that there is no uniform effective procedure…
We examine the correlation of projected rotational velocities in binary systems. It is an extension of previous work (Steinitz and Pyper, 1970; Levato, 1974). An enlarged data basis and new tests enable us to conclude that there is indeed…
Sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. Among the known sequences, cyclotomic families have the optimal autocorrelation property. In this paper, we…
We investigate the running sums of some well-known automatic sequences to determine whether they are synchronised.
Correlation between the spins (rotational velocities) in binaries has previously been established. We now continue and show that the degree of spin correlation is independent of the components' separation. Such a result might be related for…
We show that there is a very simple approach to determine the 2-adic complexity of periodic binary sequences with ideal two-level autocorrelation. This is the first main result by H. Xiong, L. Qu, and C. Li, IEEE Transactions on Information…
In this paper, a new method is presented to compute the 2-adic complexity of pseudo-random sequences. With this method, the 2-adic complexities of all the known sequences with ideal 2-level autocorrelation are uniformly determined. Results…
Binary sequences with lower autocorrelation values have important applications in cryptography and communications. In this paper, we present all possible parameters for binary periodical sequences with a 2-level autocorrelation values. For…
Correlation measure of order $k$ is an important measure of randomness in binary sequences. This measure tries to look for dependence between several shifted version of a sequence. We study the relation between the correlation measure of…
We show that it is possible to algorithmically verify if a given pattern sequence is noncorrelated. As an application, we compute that there are exactly $2272$ noncorrelated binary pattern sequences of length $\leq 4$. If we restrict our…
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…
We study the autocorrelation function of different types of eigenfunctions in quantum mechanical systems with either chaotic or mixed classical limits. We obtain an expansion of the autocorrelation function in terms of the correlation…
An infinite binary sequence is deemed to be random if it has all definable properties that hold almost surely for the usual probability measure on the set of infinite binary sequences. There are only countably many such properties, so it…
The concept of distance covariance/correlation was introduced recently to characterize dependence among vectors of random variables. We review some statistical aspects of distance covariance/correlation function and we demonstrate its…