Related papers: Aperiodic Crosscorrelation of Sequences Derived fr…
Pairs of binary sequences formed using linear combinations of multiplicative characters of finite fields are exhibited that, when compared to random sequence pairs, simultaneously achieve significantly lower mean square autocorrelation…
A pseudorandom number generator is widely used in cryptography. A cryptographic pseudorandom number generator is required to generate pseudorandom numbers which have good statistical properties as well as unpredictability. An m-sequence is…
Pseudorandom number generators are required to generate pseudorandom numbers which have good statistical properties as well as unpredictability in cryptography. An m-sequence is a linear feedback shift register sequence with maximal period…
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…
Pseudorandom sequences are used extensively in communications and remote sensing. Correlation provides one measure of pseudorandomness, and low correlation is an important factor determining the performance of digital sequences in…
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…
A collection of complex sequences of length v is complementary if the sum of their periodic autocorrelation function values at all non-zero shifts is constant. For a complex sequence A=[a_0,a_1,...,a_{v-1}] of length v=dm we define the…
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…
{\bf Abstract.} Considered is the distribution of the cross correlation between $m$-sequences of length $2^m-1$, where $m$ is even, and $m$-sequences of shorter length $2^{m/2}-1$. The infinite family of pairs of $m$-sequences with…
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…
The determination of the cross correlation between an $m$-sequence and its decimated sequence has been a long-standing research problem. Considering a ternary $m$-sequence of period $3^{3r}-1$, we determine the cross correlation…
Like other pseudorandom sequences, decimal sequences may be used in designing a Code Division Multiple Access (CDMA) system. They appear to be ideally suited for this since the cross-correlation of d-sequences taken over the LCM of their…
In this paper, we follow the recent work of Helleseth, Kholosha, Johanssen and Ness to study the cross correlation between an $m$-sequence of period $2^m-1$ and the $d$-decimation of an $m$-sequence of shorter period $2^{n}-1$ for an even…
Markov chain Monte Carlo(MCMC) is a popular approach to sample from high dimensional distributions, and the asymptotic variance is a commonly used criterion to evaluate the performance. While most popular MCMC algorithms are reversible,…
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…
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…
Binary $m$-sequences are ones with the largest period $n=2^m-1$ among the binary sequences produced by linear shift registers with length $m$. They have a wide range of applications in communication since they have several desirable…
The Pursley-Sarwate criterion of a pair of finite complex-valued sequences measures the collective smallness of the aperiodic autocorrelations and the aperiodic crosscorrelations of the two sequences. It is known that this quantity is…
We study aperiodic systems based on substitution rules by means of a transfer-matrix approach. In addition to the well-known trace map, we investigate the so-called `antitrace' map, which is the corresponding map for the difference of the…
This paper is about producing a new kind of the pairs which we call it MS-pairs. To produce these pairs, we use an algorithm for dividing a natural number $x$ by two for two arbitrary numbers and consider their related graphs. We present…