scholarly journals Some Algebraic Properties of Finite Binary Sequences

2016 ◽  
Vol 65 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Małgorzata Filipczak ◽  
Tomasz Filipczak
Keyword(s):  
Binary Sequence ◽  
Fixed Number ◽  
Binary Sequences ◽  
Algebraic Properties

Abstract We study properties of differences of finite binary sequences with a fixed number of ones, treated as binary numbers from ℤ (2m).We show that any binary sequence consisting of m terms (except of the sequence (1, 0, . . . , 0)) can be presented as a difference of two sequences having exactly n ones, whenever .

scholarly journals Quasi-Random Graphs, Pseudo-Random Graphs and Pseudorandom Binary Sequences, I. (Quasi-Random Graphs)

2019 ◽  
Vol 14 (2) ◽  
pp. 103-126
Author(s):  
József Borbély ◽  
András Sárközy
Keyword(s):  
Random Graphs ◽  
Adjacency Matrix ◽  
Binary Sequence ◽  
Binary Sequences ◽  
Circulant Graph ◽  
Large Families

AbstractIn the last decades many results have been proved on pseudo-randomness of binary sequences. In this series our goal is to show that using many of these results one can also construct large families of quasi-random, pseudo-random and strongly pseudo-random graphs. Indeed, it will be proved that if the first row of the adjacency matrix of a circulant graph forms a binary sequence which possesses certain pseudorandom properties (and there are many large families of binary sequences known with these properties), then the graph is quasi-random, pseudo-random or strongly pseudo-random, respectively. In particular, here in Part I we will construct large families of quasi-random graphs along these lines. (In Parts II and III we will present and study constructions for pseudo-random and strongly pseudo-random graphs, respectively.)

Concatenation of Legendre symbol sequences

2011 ◽  
Vol 48 (2) ◽  
pp. 193-204
Author(s):  
Katalin Gyarmati
Keyword(s):  
Binary Sequence ◽  
Binary Sequences ◽  
Legendre Symbol ◽  
Pseudorandom Binary Sequence ◽  
Symbol Sequences

In the applications it may occur that our initial pseudorandom binary sequence is not long enough, thus we have to take the concatenation of it with another pseudorandom binary sequences. Here we will consider concatenation of Legendre symbol sequences so that the resulting longer sequence has strong pseudorandom properties.

scholarly journals On the Design of Soret Zone Plates Based on Binary Sequences Using Directional Transducers

Sensors ◽  
2021 ◽  
Vol 21 (18) ◽  
pp. 6086
Author(s):  
Pilar Candelas ◽  
Sergio Pérez-López ◽  
José Miguel Fuster
Keyword(s):  
Theoretical Model ◽  
Enhancement Factor ◽  
Critical Parameter ◽  
Binary Sequence ◽  
Transmission Efficiency ◽  
Binary Sequences ◽  
Experimental Measurements ◽  
Zone Plates

In this work, we analyze the effect of the distribution of transparent Fresnel regions over the focusing profile of Soret Zone Plates (SZP) based on binary sequences. It is shown that this effect becomes very significant in those fields where directional transducers are employed, such as microwaves or acoustics. A thorough analysis of both the SZP transmission efficiency and the focusing enhancement factor is presented. Moreover, experimental measurements are also carried out for a particular type of binary sequence, the Cantor ternary set, validating the theoretical model and demonstrating that the distribution of transparent Fresnel regions becomes a critical parameter in applications requiring directional emitters.

scholarly journals On the stability of periodic binary sequences with zone restriction

2020 ◽  
Author(s):  
Ming Su ◽  
Qiang Wang
Keyword(s):  
Global Stability ◽  
Local Stability ◽  
Linear Complexity ◽  
Binary Sequence ◽  
Search Space ◽  
Binary Sequences ◽  
Zone Length ◽  
Stability Measure ◽  
Error Linear Complexity ◽  
The Stability

Abstract 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. For several classes of sequences, we demonstrate that the k-error linear complexity is identical to the k-error linear complexity within a zone, while the length of a zone is much smaller than the whole period when the k-error linear complexity is large. These sequences have periods $$2^n$$ 2 n , or $$2^v r$$ 2 v r (r odd prime and 2 is primitive modulo r), or $$2^v p_1^{s_1} \cdots p_n^{s_n}$$ 2 v p 1 s 1 ⋯ p n s n ($$p_i$$ p i is an odd prime and 2 is primitive modulo $$p_i^2$$ p i 2 , where $$1\le i \le n$$ 1 ≤ i ≤ n ) respectively. In particular, we completely determine the spectrum of 1-error linear complexity with any zone length for an arbitrary $$2^n$$ 2 n -periodic binary sequence.

scholarly journals Design of Binary-Sequence Zone Plates in High Wavelength Domains

Sensors ◽  
2018 ◽  
Vol 18 (8) ◽  
pp. 2604 ◽  
Author(s):  
José Fuster ◽  
Sergio Pérez-López ◽  
Pilar Candelas ◽  
Constanza Rubio
Keyword(s):  
Design Method ◽  
Binary Sequence ◽  
Additional Term ◽  
Binary Sequences ◽  
X Rays ◽  
Zone Plates ◽  
Acoustic Focusing ◽  
Sequence Method ◽  
High Flexibility ◽  
High Wavelength

The design of zone plates is an important topic in many areas of physics, such as optics, X-rays, microwaves or ultrasonics. In this paper, a zone plate design method, which provides high flexibility in the shaping of the focusing profile, is analyzed. This flexibility is achieved through the use of binary sequences that produce zone plates with different properties and applications. It is shown that this binary-sequence method works properly at low wavelengths, but requires a modification term to work accurately in high wavelength domains. This additional term extends this powerful design method to any wavelength. Simulation results show acoustic focusing profiles for Fresnel, Fibonacci and Cantor zone plates operating at a wavelength of 1.5 mm without any distortion.

scholarly journals Random Binary Sequences in Telecommunications

2013 ◽  
Vol 64 (4) ◽  
pp. 230-237 ◽  
Author(s):  
Slavko Šajić ◽  
Nebojša Maletić ◽  
Branislav M. Todorović ◽  
Milan Šunjevarić
Keyword(s):  
Random Sequence ◽  
Binary Sequence ◽  
Statistical Test ◽  
Binary Sequences ◽  
Secure Communications ◽  
Basic Principles ◽  
Sequence Generation ◽  
Telecommunication Systems ◽  
Random Sequence Generation ◽  
Insight Into

Realization of modern telecommunication systems is inconceivable without use of different binary sequences. In this paper, an overview of random binary sequences used in different telecommunication systems is given. Basic principles of pseudorandom, chaotic, and true random sequence generation are presented, as well as their application in telecommunications in respect to advantages and drawbacks of the same. Moreover, particular scheme for true random binary sequence generation is given, as well as results of randomness assessment obtained by NIST statistical test suite. Finally, short insight into importance of random binary sequence in secure communications is given.

scholarly journals On Sequence Lengths of Some Special External Exclusive OR Type LFSR Structures – Study and Analysis

2014 ◽  
Vol 11 (2) ◽  
pp. 1 ◽  
Author(s):  
A Ahmad ◽  
A Al Maashri
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Binary Sequence ◽  
Binary Sequences ◽  
Linear Feedback ◽  
Complex Task ◽  
Linear Feedback Shift Registers ◽  
Feedback Shift Registers ◽  
Self Test ◽  
Exclusive Or

The study of the length of pseudo-random binary sequences generated by Linear- Feedback Shift Registers (LFSRs) plays an important role in the design approaches of built-in selftest, cryptosystems, and other applications. However, certain LFSR structures might not be appropriate in some situations. Given that determining the length of generated pseudo-random binary sequence is a complex task, therefore, before using an LFSR structure, it is essential to investigate the length and the properties of the sequence. This paper investigates some conditions and LFSR’s structures, which restrict the pseudo-random binary sequences’ generation to a certain fixed length. The outcomes of this paper are presented in the form of theorems, simulations, and analyses. We believe that these outcomes are of great importance to the designers of built-in self-test equipment, cryptosystems, and other applications such as radar, CDMA, error correction, and Monte Carlo simulation. 

scholarly journals Binary sequences and lattices constructed by discrete logarithms

2021 ◽  
Vol 7 (3) ◽  
pp. 4655-4671
Author(s):  
Yuchan Qi ◽  
◽  
Huaning Liu
Keyword(s):  
Exponential Sums ◽  
Binary Sequence ◽  
Large Family ◽  
Binary Sequences ◽  
Multiplicative Inverse ◽  
Discrete Logarithms ◽  
Modulo P ◽  
Large Families ◽  
Definition Of ◽  
Pseudorandom Measures

<abstract><p>In 1997, Mauduit and Sárközy first introduced the measures of pseudorandomness for binary sequences. Since then, many pseudorandom binary sequences have been constructed and studied. In particular, Gyarmati presented a large family of pseudorandom binary sequences using the discrete logarithms. Ten years later, to satisfy the requirement from many applications in cryptography (e.g., in encrypting "bit-maps'' and watermarking), the definition of binary sequences is extended from one dimension to several dimensions by Hubert, Mauduit and Sárközy. They introduced the measure of pseudorandomness for this kind of several-dimension binary sequence which is called binary lattices. In this paper, large families of pseudorandom binary sequences and binary lattices are constructed by both discrete logarithms and multiplicative inverse modulo $ p $. The upper estimates of their pseudorandom measures are based on estimates of either character sums or mixed exponential sums.</p></abstract>

Steganographic capacity for one-dimensional Markov cover

2017 ◽  
Vol 27 (4) ◽  
Author(s):  
Valeriy A. Voloshko
Keyword(s):  
Binary Sequence ◽  
Binary Sequences ◽  
Probability Measures ◽  
One Dimensional

Abstract For shift-invariant probability measures on the set of infinite two-sided binary sequences (one-dimensional covers) we introduce the notion of capacity as a maximum portion of embedded into the cover uniformly distributed (purely random) binary sequence (message) that admits special correction of the cover restoring its distribution up to distribution of

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