Related papers: Linear Complexity of Binary Interleaved Sequences …
Binary Whiteman's cyclotomic sequences of orders 2 and 4 have a number of good randomness properties. In this paper, we compute the autocorrelation values and linear complexity of the first class two-prime Whiteman's generalized cyclotomic…
Traditional global stability measure for sequences is hard to determine because of large search space. We propose the $k$-error linear complexity with a zone restriction for measuring the local stability of sequences. Accordingly, we can…
Due to wide applications of binary sequences with low correlation to communications, various constructions of such sequences have been proposed in literature. However, most of the known constructions via finite fields make use of the…
Binary self-dual sequences have been considered and analyzed throughout the years, and they have been used for various applications. Motivated by a construction for single-track Gray codes, we examine the structure and recursive…
We present a complete classification of the deterministic distributed time complexity for a family of graph problems: binary labeling problems in trees. These are locally checkable problems that can be encoded with an alphabet of size two…
The problem of efficiently characterizing degree sequences of simple hypergraphs is a fundamental long-standing open problem in Graph Theory. Several results are known for restricted versions of this problem. This paper adds to the list of…
In this paper, we construct two generalized cyclotomic binary sequences of period $2p^{m}$ based on the generalized cyclotomy and compute their linear complexity, showing that they are of high linear complexity when $m\geq 2$.
In the realm of modern digital communication, cryptography, and signal processing, binary sequences with a low correlation properties play a pivotal role. In the literature, considerable efforts have been dedicated to constructing good…
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…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
The problem of finding aperiodic low auto-correlation binary sequences (LABS) presents a significant computational challenge, particularly as the sequence length increases. Such sequences have important applications in communication…
Let $q=p^r$ be a power of an odd prime $p$. We study binary sequences $\sigma=(\sigma_0,\sigma_1,\ldots)$ with entries in $\{0,1\}$ defined by using the quadratic character $\chi$ of the finite field $\mathbb{F}_q$: $$ \sigma_n=\left\{…
The linear complexity and the $k$-error linear complexity of a binary sequence are important security measures for key stream strength. By studying binary sequences with the minimum Hamming weight, a new tool named as hypercube theory is…
Binary sequences with low autocorrelations are important in communication engineering and in statistical mechanics as groundstates of the Bernasconi-model. Computer searches are the main tool to construct such sequences. Due to the…
We consider the $k$-error linear complexity of a new binary sequence of period $p^2$, proposed in the recent paper "New generalized cyclotomic binary sequences of period $p^2$", by Z. Xiao et al., who calculated the linear complexity of the…
The search for binary sequences with a high figure of merit, known as the low autocorrelation binary sequence ($labs$}) problem, represents a formidable computational challenge. To mitigate the computational constraints of the problem, we…
The linear complexity of a periodic sequence over $GF(p^m)$ plays an important role in cryptography and communication [12]. In this correspondence, we prove a result which reduces the computation of the linear complexity and minimal…
We identify a binary sequence $\mathcal{S}=(s_n)_{n=0}^\infty$ with the $2$-adic integer $G_\mathcal{S}(2)=\sum\limits_{n=0}^\infty s_n2^n$. In the case that $G_\mathcal{S}(2)$ is algebraic over $\mathbb{Q}$ of degree $d\ge 2$, we prove…
Consider words of length $n$. The set of all periods of a word of length $n$ is a subset of $\{0,1,2,\ldots,n-1\}$. However, any subset of $\{0,1,2,\ldots,n-1\}$ is not necessarily a valid set of periods. In a seminal paper in 1981, Guibas…
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…