Related papers: Algorithmic classification of noncorrelated binary…
In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
Certain applications require the use of signals that combine both the capability to operate with low signal-to-noise ratios and the ability to support multiple users without interference. In the case where many users have very different…
A Barker sequence is a binary sequence for which all nontrivial aperiodic autocorrelations are either 0, 1 or -1. The only known Barker sequences have length 2, 3, 4, 5, 7, 11 or 13. It is an old conjecture that no longer Barker sequences…
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…
Aperiodic autocorrelation is an important indicator of performance of sequences used in communications, remote sensing, and scientific instrumentation. Knowing a sequence's autocorrelation function, which reports the autocorrelation at…
Nonlinear complexity, as an important measure for assessing the randomness of sequences, is defined as the length of the shortest feedback shift registers that can generate a given sequence. In this paper, the structure of n-periodic binary…
In this paper, we present a computational search for best-known merit factors of longer binary sequences with an odd length. Finding low autocorrelation binary sequences with optimal or suboptimal merit factors is a very difficult…
We consider two algorithms which can be used for proving positivity of sequences that are defined by a linear recurrence equation with polynomial coefficients (P-finite sequences). Both algorithms have in common that while they do succeed…
We estimate the maximum-order complexity of a binary sequence in terms of its correlation measures. Roughly speaking, we show that any sequence with small correlation measure up to a sufficiently large order $k$ cannot have very small…
Given several number sequences, determining the longest common subsequence is a classical problem in computer science. This problem has applications in bioinformatics, especially determining transposable genes. Nevertheless, related works…
We propose new concepts in order to analyze and model the dependence structure between two time series. Our methods rely exclusively on the order structure of the data points. Hence, the methods are stable under monotone transformations of…
We study pattern densities in binary sequences, finding optimal limit sequences with fixed pattern densities.
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…
The in-depth analysis of time series has gained a lot of research interest in recent years, with the identification of periodic patterns being one important aspect. Many of the methods for identifying periodic patterns require time series'…
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…
Two objects are independent if they do not affect each other. Independence is well-understood in classical information theory, but less in algorithmic information theory. Working in the framework of algorithmic information theory, the paper…
A family of binary sequences is presented and proved to have optimal correlation property and large linear span. It includes the small set of Kasami sequences, No sequence set and TN sequence set as special cases. An explicit lower bound…
The linear complexity of a sequence $s$ is one of the measures of its predictability. It represents the smallest degree of a linear recursion which the sequence satisfies. There are several algorithms to find the linear complexity of a…
Proving programs terminating is a fundamental computer science challenge. Recent research has produced powerful tools that can check a wide range of programs for termination. The analog for probabilistic programs, namely termination with…
All codes with minimum distance 8 and codimension up to 14 and all codes with minimum distance 10 and codimension up to 18 are classified. Nonexistence of codes with parameters [33,18,8] and [33,14,10] is proved. This leads to 8 new exact…