Related papers: Algorithmic classification of noncorrelated binary…
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…
We prove a conjecture that classifies exceptional numbers. This conjecture arises in two different ways, from cryptography and from coding theory. An odd integer $t\geq 3$ is said to be exceptional if $f(x)=x^t$ is APN (Almost Perfect…
An inversion sequence of length $n$ is an integer sequence $(a_1, \ldots, a_n)$ such that $0 \le a_i < i$ for all $i$. The study of pattern-avoiding inversion sequences was initiated in 2015 by Mansour and Shattuck and in 2016 by Corteel,…
We consider the problem of identifying tandem scattered subsequences within a string. Our algorithm identifies a longest subsequence which occurs twice without overlap in a string. This algorithm is based on the Hunt-Szymanski algorithm,…
The $2$-adic complexity has been well-analyzed in the periodic case. However, we are not aware of any theoretical results on the $N$th $2$-adic complexity of any promising candidate for a pseudorandom sequence of finite length $N$ or…
Binary code similarity detection is to detect the similarity of code at binary (assembly) level without source code. Existing works have their limitations when dealing with mutated binary code generated by different compiling options. In…
In Linear Algebra over finite fields, a characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold…
A method for estimating the merit factors of sequences will be provided. The result is also effective in determining the nonexistence of certain infinite collections of cyclic difference sets and cyclic matrices and associated binary…
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…
The investigation of Bell nonlocality traditionally relies on joint probabilities of observing certain measurement outcomes. In this work we explore a possibilistic approach, where only patterns of possible outcomes matter, and apply it to…
The merit factor problem is of practical importance to manifold domains, such as digital communications engineering, radars, system modulation, system testing, information theory, physics, chemistry. However, the merit factor problem is…
In this work, a classical problem of the digital sequence design, or more precisely, finding binary sequences with optimal peak sidelobe level (PSL), is revisited. By combining some of our previous works, together with some mathematical…
We consider packing tree degree sequences in this paper. We set up a conjecture that any arbitrary number of tree degree sequences without common leaves have edge disjoint tree realizations. This conjecture is known to be true for $2$ and…
In this note, we consider the problem of counting and verifying abelian border arrays of binary words. We show that the number of valid abelian border arrays of length \(n\) is \(2^{n-1}\). We also show that verifying whether a given array…
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
We propose a class of continuous-time Markov counting processes for analyzing correlated binary data and establish a correspondence between these models and sums of exchangeable Bernoulli random variables. Our approach generalizes many…
Using an asymmetric associative network with synchronous updating, it is possible to recall a sequence of patterns. To obtain a stable sequence generation with a large storage capacity, we introduce a threshold that eliminates the…
In this paper, necessary and sufficient conditions for a cyclic code of arbitrary length over the non-chain rings $Z_{4}+\nu Z_{4}$ for $\nu^{2} \in \{0,1,\nu,2\nu,3\nu,2+\nu,2+3\nu,3+2\nu\}$ to be a reversible cyclic code have been…
Elementary cellular automata deterministically map a binary sequence to another using simple local rules. Visualizing the structure of this mapping is difficult because the number of nodes (i.e. possible binary sequences) grows…
With the increased availability of quantum technological devices, it becomes more important to have tools to guarantee their correct nonclassical behavior. This is especially important for quantum networks, which constitute the platforms…