Related papers: Orientable and negative orientable sequences
Imperative programmers often use cyclically linked trees in order to achieve O(1) navigation time to neighbours. Some logic programmers believe that cyclic terms are necessary to achieve the same in logic-based languages. An old but…
A de Bruijn torus is the two dimensional generalization of a de Bruijn sequence. While some methods exist to generate these tori, only a few methods of construction are known. We present a novel method to generate de Bruijn tori with…
Binary sequences with optimal autocorrelation and large linear complexity have important applications in cryptography and communications. Very recently, a class of binary sequences of period $4p$ with optimal autocorrelation was proposed…
The binary expansions of irrational algebraic numbers can serve as high-quality pseudorandom binary sequences. This study presents an efficient method for computing the exact binary expansions of real quadratic algebraic integers using…
We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a…
Autoregressive models have proven to be very powerful in NLP text generation tasks and lately have gained popularity for image generation as well. However, they have seen limited use for the synthesis of 3D shapes so far. This is mainly due…
Boolean functions and binary sequences are main tools used in cryptography. In this work, we introduce a new bijection between the set of Boolean functions and the set of binary sequences with period a power of two. We establish a…
This paper presents a method to find new De Bruijn cycles based on ones of lesser order. This is done by mapping a De Bruijn cycle to several vertex disjoint cycles in a De Bruijn digraph of higher order and connecting these cycles into one…
We present an algorithm for effectively generating binary sequences which would be rated by people as highly likely to have been generated by a random process, such as flipping a fair coin.
A sequence of non-negative integers is called a B_k sequence if all the sums of arbitrary k elements are different. In this paper, we will present a new estimation for the upper bound of B_k sequences.
Sidon sequences and their generalizations have found during the years and especially recently various applications in coding theory. One of the most important applications of these sequences is in the connection of synchronization patterns.…
We develop constructions for exchangeable sequences of point processes that are rendered conditionally-i.i.d. negative binomial processes by a (possibly unknown) random measure called the base measure. Negative binomial processes are useful…
Sequence-to-sequence neural networks have been widely used in language-based applications as they have flexible capabilities to learn various language models. However, when seeking for the optimal language response through trained neural…
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…
The run vector of a binary sequence reflects the run structure of the sequence, which is given by the set of all substrings of the run length encoding. The run vector and the aperiodic autocorrelations of a binary sequence are strongly…
In this paper, we consider the problem of constructing optimal average-length binary codes under the constraint that each codeword must contain at most $D$ ones, where $D$ is a given input parameter. We provide an $O(n^2D)$-time complexity…
A data structure for finite bounded acyclic categories has been built, which is useful to encode and manipulate abstract orientable incidence structure. It can be represented as a directed acyclic multigraph with weighted edges, where the…
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…
We construct a pseudorandom generator which fools read-$k$ oblivious branching programs and, more generally, any linear length oblivious branching program, assuming that the sequence according to which the bits are read is known in advance.…
The discrepancy of a binary string is the maximum (absolute) difference between the number of ones and the number of zeroes over all possible substrings of the given binary string. In this note we determine the minimal discrepancy that a…