Construction Of Binary Sequences Research Articles

Linear complexity and 2-adic complexity of binary interleaved sequences with optimal autocorrelation magnitude

<abstract><p>A construction of binary sequences with period $ 4N $ and optimal autocorrelation magnitude has been investigated based on sampling and interleaving technique. We determine the exact value of the linear complexity of the constructed sequences according to the deep relationship among the characteristic polynomials, and show it is $ 2N+2 $. Moreover, we determine the 2-adic complexity of these sequences by the autocorrelation function, and show it can attain the maximum value. Results show that such sequences can resist both the Berlekamp-Massey attack and the Rational Approximation Algorithm, in addition are good for communication.</p></abstract>

2-Adic complexity of two constructions of binary sequences with period 4N and optimal autocorrelation magnitude

2-Adic complexity of two constructions of binary sequences with period 4N and optimal autocorrelation magnitude

Construction of Binary Sequences With Low Correlation via Multiplicative Quadratic Character Over Finite Fields of Odd Characteristics

In literature, there are several methods to construct Gold sequences. One of the constructions is via the trace function from extension field of \mathbb F <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> . Estimation of correlation of this construction is based on number of rational points of elliptic curves. In this article, we generalize this construction from finite fields of even characteristic to odd characteristics by using multiplicative quadratic character. Again, estimation of correlation of this construction is based on number of rational points of elliptic curves. Thus, we obtain binary sequences which have more flexibility on length while still possessing low correlation property. Moreover, some of the sequences are optimally balanced.

Generic Construction of Binary Sequences of Period $2N$ With Optimal Odd Correlation Magnitude Based on Quaternary Sequences of Odd Period $N$

Binary sequences with low odd correlation have important applications in communication systems to reduce interference. In this paper, using the interleaving technique, we present a generic connection between binary sequences with low odd correlation and quaternary sequences with low even correlation. As a result, some new binary sequences with optimal odd auto-correlation magnitude are obtained. Besides, two sets consisting of $2^{n}+1$ binary sequences of period $2(2^{n}-1)$ with the maximum odd correlation magnitude $2^{((n+1)/ 2)}+2$ are derived, which are the first two optimal classes of binary sequence sets achieving the Sarwate bound on the odd correlation magnitude in the literature.

Two constructions of binary sequences with optimal autocorrelation magnitude

In this Letter, two constructions of new binary sequences with optimal autocorrelation magnitude of length 4N derived from binary sequences with optimal autocorrelation of length N = 2 (mod 4) and almost-perfect binary sequences of length 2N using N × 2 interleaved structure is presented. The first construction is to use binary Sidelnikov sequences of length N = pn −1 whereas the second one is to use binary Ding–Helleseth–Martinsen sequences of length N = 2p. The obtained sequences have large linear complexity and can be used in communication and cryptography.

On pseudorandom binary sequences constructed by using finite fields

By using finite fields of order \(p^r\) with \(r \ge 2\) and their quadratic characters, Sarkozy and Winterhof presented a construction for binary sequences of length \(p^r\) with strong pseudorandom properties. In the special case \(r=2\) Gyarmati improved on their estimates for the pseudorandom measures of these sequences. Here we extend Gyarmati’s result and sharpen the estimates of Sarkozy and Winterhof for any prime power \(p^r\).

On the Construction of Binary Sequence Families With Low Correlation and Large Sizes

In this paper, we revisit a method to produce binary sequences using the most significant bit map from Z4 to the binary field. This method is useful for the construction of binary sequences with low correlation and large family size. There may be more cases where starting with Z4 could help researchers design new low correlation sequences for code-division multiple access application.

Constructions of Binary Sequences with Almost Optimal Autocorrelation Magnitude

Constructions of Binary Sequences with Almost Optimal Autocorrelation Magnitude

New Constructions of Binary Sequences with Optimal Autocorrelation Magnitude Based on Interleaving Technique

Recently, Yu, Gong and Tang found new constructions of binary sequences of period 4N with optimal autocorrelation magnitude by different interleaved structure of sequences and sequences which had special correlation property, respectively. In this paper, we derive more results on binary sequences of period 4N which also have optimal autocorrelation.

New Constructions of Binary Sequences with Good Autocorrelation Based on Interleaving Technique

In this paper, we propose new constructions of binary sequences based on an interleaving technique. In our constructions, we make use of any binary sequences with ideal 2-level autocorrelation, a special shift sequence as well as the perfect binary sequence or sequence (0,1,1) in the interleaved structure to get the new sequences. Except for the most autocorrelation values of our new sequences, we find that the unexpected autocorrelation values only occur four or two times in each period no matter how long the period is. We state that the sequences have a good autocorrelation in this case. In particular, the autocorrelation distribution of our sequences is determined.

The Linear Complexity of Binary Sequences With Optimal Autocorrelation

Binary sequences with optimal autocorrelation are needed in many applications. Two constructions of binary sequences with optimal autocorrelation of period N ≡ 0 (mod 4) are investigated. The two constructions are powerful and generic in the sense that many classes of binary sequences with optimal autocorrelation could be obtained from binary sequences with ideal autocorrelation. General results on the minimal polynomials of these binary sequences are derived. Based on the results, both the linear complexities and the minimal polynomials are determined.

The Linear Complexity of Some Binary Sequences With Three-Level Autocorrelation

Binary sequences with good autocorrelation are needed in many applications. A construction of binary sequences with three-level autocorrelation was recently presented. This construction is generic and powerful in the sense that many classes of binary sequences with three-level autocorrelation could be obtained from any difference set with Singer parameters. The objective of this paper is to determine both the linear complexity and the minimal polynomial of two classes of binary sequences, i.e., the class based on the Singer difference set, and the class based on the GMW difference set.

Constructions of binary sequences with optimal autocorrelation value

A new class of binary sequence of period 4N with optimal autocorrelation value is constructed. According to the relation between sequence with optimal autocorrelation value and almost difference set, a new almost difference set is also derived.

Finding low autocorrelation binary sequences with memetic algorithms

This paper deals with the construction of binary sequences with low autocorrelation, a very hard problem with many practical applications. The paper analyzes several metaheuristic approaches to tackle this kind of sequences. More specifically, the paper provides an analysis of different local search strategies, used as stand-alone techniques and embedded within memetic algorithms. One of our proposals, namely a memetic algorithm endowed with a Tabu Search local searcher, performs at the state-of-the-art, as it consistently finds optimal sequences in considerably less time than previous approaches reported in the literature. Moreover, this algorithm is also able to provide new best-known solutions for large instances of the problem. In addition, a variant of this algorithm that explores only a promising subset of the whole search space (known as skew-symmetric sequences) is also analyzed. Experimental results show that this new algorithm provides new best-known solutions for very large instances of the problem.

On the search for low correlated binary sequences

The construction of binary sequences with low aperiodic correlation is one of the most famous, but also one of the most challenging, problems in signal design theory. In recent decades, many approaches from different mathematical disciplines have been used to tackle the problem. This paper summarizes the known results and adds some new results on the peak correlation of extended Legendre sequences and on binary arrays.

On the Linear Complexity of the Sidelnikov-Lempel-Cohn-Eastman Sequences

In [6] and [10], a construction of binary sequences with an (almost) optimal autocorrelation spectrum is suggested. We continue the study of the linear complexity and the linear feedback polynomial of these sequences over \Bbb{F}2, originated in [4].