Related papers: Arithmetic autocorrelation distribution of binary …
An $m$-sequence is the one of the largest period among those produced by a linear feedback shift register. It possesses several desirable features of pseudorandomness such as balance, uniform pattern distribution and ideal autocorrelation…
The (classical) crosscorrelation is an important measure of pseudorandomness of two binary sequences for applications in communications. The arithmetic crosscorrelation is another figure of merit introduced by Goresky and Klapper…
Binary periodic sequences with good autocorrelation property have many applications in many aspects of communication. In past decades many series of such binary sequences have been constructed. In the application of cryptography, such…
The extent to which a sequence of finite length differs from a shifted version of itself is measured by its aperiodic autocorrelations. Of particular interest are sequences whose entries are 1 or -1, called binary sequences, and sequences…
The arithmetic crosscorrelation of binary $m$-sequences with coprime periods $2^{n_1}-1$ and $2^{n_2}-1$\ ($\gcd(n_1,n_2)=1$) is determined. The result shows that the absolute value of arithmetic crosscorrelation of such binary…
Binary sequences with optimal autocorrelation play important roles in radar, communication, and cryptography. Finding new binary sequences with optimal autocorrelation has been an interesting research topic in sequence design.…
The autocorrelation and the linear complexity of a key stream sequence in a stream cipher are important cryptographic properties. Many sequences with these good properties have interleaved structure, three classes of binary sequences of…
Pseudo-random sequences with good statistical property, such as low autocorrelation, high linear complexity and large 2-adic complexity, have been applied in stream cipher. In general, it is difficult to give both the linear complexity and…
Binary sequences with minimal autocorrelations have applications in communication engineering, mathematics and computer science. In statistical physics they appear as groundstates of the Bernasconi model. Finding these sequences is a…
Sequences with good randomness properties are quite important for stream ciphers. In this paper, a new class of quaternary sequences is constructed by using generalized cyclotomic classes of $\mathbb{Z}_{2p^m}$ $(m\geq1)$. The exact values…
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…
A general construction of binary sequences with low autocorrelation are considered in the paper. Based on recent progresses about this topic and this construction, several classes of binary sequences with optimal autocorrelation and other…
It is shown that a random binary process with impulse-like autocorrelation can be generated by randomizing the length of symbols occurring in a random Bernoulli process. Such randomization is achieved by random (or judiciously designed…
Aperiodic autocorrelation is an important indicator of performance of sequences used in communications, remote sensing, and scientific instrumentation. Knowing a sequence's autocorrelation function, which reports the autocorrelation at…
We analyze the connection between the autocorrelation of a binary sequence and its run structure given by the run length encoding. We show that both the periodic and the aperiodic autocorrelation of a binary sequence can be formulated in…
Constructions of binary sequences with low autocorrelation are considered in the paper. Based on recent progresses about this topic, several more general constructions of binary sequences with optimal autocorrelations and other low…
The autocorrelation function and the run structure are two basic notions for binary sequences, and have been used as two independent postulates to test randomness of binary sequences ever since Golomb 1955. In this paper, we prove for…
LSB (Least Significant Bit) sequences are widely used as the initial inputs in some modern stream ciphers, such as the ZUC algorithm-the core of the 3GPP LTE International Encryption Standard. Therefore, analyzing the statistical properties…
Maximum-length sequences (m-sequences for short) over finite fields are generated by linear feedback shift registers with primitive characteristic polynomials. These sequences have nice mathematical structures and good randomness properties…
Considered is the distribution of the crosscorrelation between $m$-sequences of length $2^m-1$, where $m=2k$, and $m$-sequences of shorter length $2^k-1$. New pairs of $m$-sequences with three-valued crosscorrelation are found and the…