Related papers: Binary sequences with length n and nonlinear compl…
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…
An algorithm for constructing a shortest binary k-stage machine generating a given binary sequence is presented. This algorithm can be considered as an extension of Berlekamp-Massey algorithm to the non-linear case.
Given two {0,1}-sequences X and Y of lengths m and n, respectively, we write L(X,Y) to denote the length of the longest common subsequence (LCS) of X and Y, and write L(m,n) to denote the expected value of L(X,Y) when X and Y are random…
An infinite binary sequence is Bennett deep if, for any computable time bound, the difference between the time-bounded prefix-free Kolmogorov complexity and the prefix-free Kolmogorov complexity of its initial segments is eventually…
An efficient algorithm for classification of binary self-dual codes is presented. As an application, a complete classification of the self-dual codes of length 38 is given.
The discrepancy of a binary string refers to the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. We provide an investigation of the discrepancy of…
Two series of binary observations $x_1,x_1,...$ and $y_1,y_2,...$ are presented: at each time $n\in\N$ we are given $x_n$ and $y_n$. It is assumed that the sequences are generated independently of each other by two B-processes. We are…
Some mutually quasi-unbiased weighing matrices are constructed from binary codes satisfying certain conditions. Motivated by this, in this note, we study binary codes satisfying the conditions. The weight distributions of binary codes…
We study the worst-case complexity of a non-monotone line search framework that covers a wide variety of known techniques published in the literature. In this framework, the non-monotonicity is controlled by a sequence of nonnegative…
Sequences with high linear complexity have wide applications in cryptography. In this paper, a new class of quaternary sequences over $\mathbb{F}_4$ with period $2p^mq^n$ is constructed using generalized cyclotomic classes. Results show…
A complete classification of binary doubly even self-dual codes of length 40 is given. As a consequence, a classification of binary extremal self-dual codes of length 38 is also given.
Binary cyclic codes are worth studying due to their applications and theoretical importance. It is an important problem to construct an infinite family of cyclic codes with large minimum distance $d$ and dual distance $d^{\perp}$. In recent…
We study cyclic binary strings with bounds on the lengths of the intervals of consecutive ones and zeros. This is motivated by scheduling problems where such binary strings can be used to represent the state (on/off) of a machine. In this…
Analogously to de Bruijn sequences, orientable sequences have application in automatic position-location applications and, until recently, studies of these sequences focused on the binary case. In recent work by Alhakim et al., a range of…
In this paper we construct an infinite sequence of binary irreducible polynomials starting from any irreducible polynomial $f_0 \in \F_2 [x]$. If $f_0$ is of degree $n = 2^l \cdot m$, where $m$ is odd and $l$ is a non-negative integer,…
In parametric sequence alignment, optimal alignments of two sequences are computed as a function of the penalties for mismatches and spaces, producing many different optimal alignments. Here we give a 3/(2^{7/3}\pi^{2/3})n^{2/3} +O(n^{1/3}…
We provide a combinatorial construction for linear codes attaining the maximum possible number of distinct weights. We then introduce the related problem of determining the existence of linear codes with an arbitrary number of distinct…
Given a barrier $0 \leq b_0 \leq b_1 \leq ...$, let $f(n)$ be the number of nondecreasing integer sequences $0 \leq a_0 \leq a_1 \leq ... \leq a_n$ for which $a_j \leq b_j$ for all $0 \leq j \leq n$. Known formul\ae for $f(n)$ include an $n…
Given a set of sequences, the distance between pairs of them helps us to find their similarity and derive structural relationship amongst them. For genomic sequences such measures make it possible to construct the evolution tree of…
A new class of linear sequence generators based on cellular automata is here introduced in order to model several nonlinear keystream generators with practical applications in symmetric cryptography. The output sequences are written as…