Related papers: Sequences with thirteen-valued cross correlations

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…

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…

Let $n=2m$, $m$ odd, $e|m$, and $p$ odd prime with $p\equiv1\ \mathrm{mod}\ 4$. Let $d=\frac{(p^{m}+1)^{2}}{2(p^{e}+1)}$. In this paper, we study the cross-correlation between a $p$-ary $m$-sequence $\{s_{t}\}$ of period $p^{2m}-1$ and its…

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…

Let $d=\frac{(3^{2k}+1)^{2}}{20}$, where $k$ is an odd integer. We show that the magnitude of the cross-correlation values of a ternary $m$-sequence $\{s_{t}\}$ of period $3^{4k}-1$ and its decimated sequence $\{s_{dt}\}$ is upper bounded…

{\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…

For an odd prime $p$ and $n=2m$, a new decimation $d=\frac{(p^{m}-1)^{2}}{2}+1$ of Niho type of $m$-sequences is presented. Using generalized Niho's Theorem, we show that the cross-correlation function between a $p$-ary $m$-sequence of…

For the complete five-valued cross-correlation distribution between two $m$-sequences ${s_t}$ and ${s_{dt}}$ of period $2^m-1$ that differ by the decimation $d={{2^{2k}+1}\over {2^k+1}}$ where $m$ is odd and $\mbox{gcd}(k,m)=1$, Johansen…

In this paper, for an odd prime $p$ such that $p\equiv 3\bmod 4$, odd $n$, and $d=(p^n+1)/(p^k+1)+(p^n-1)/2$ with $k|n$, the value distribution of the exponential sum $S(a,b)$ is calculated as $a$ and $b$ run through $\mathbb{F}_{p^n}$. The…

In this paper, let $n=2m$ and $d=3^{m+1}-2$ with $m\geq2$ and $\gcd(d,3^n-1)=1$. By studying the weight distribution of the ternary Zetterberg code and counting the numbers of solutions of some equations over the finite field…

The cross-correlation problem is a classic problem in sequence design. In this paper we compute the cross-correlation distribution of the Niho-type decimation $d=3(p^m-1)+1$ over $\mathrm{GF}(p^{2m})$ for any prime $p \ge 5$. Previously…

In this paper, new pairs of binary sequences with three cross correlation values are presented. The cross correlation values are shown to be low. Finally we present some numerical results and some open problems.

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…

We consider the problem of determining the cross-correlation values of the sequences in the families comprised of constant multiples of $M$-ary Sidelnikov sequences over $\mathbb{F}_q$, where $q$ is a power of an odd prime $p$. We show that…

We exploit Krattenthaler's bijection between the set $S_n(3\textrm{-}1\textrm{-}2)$ of permutations in $S_n$ avoiding the classical pattern $3\textrm{-}1\textrm{-}2$ and Dyck $n$-paths to study the distribution of every consecutive pattern…

A sequence $(x_n)_{n=1}^{\infty}$ on the torus $\mathbb{T}$ exhibits Poissonian pair correlation if for all $s\geq0$, \begin{equation*} \lim_{N\to\infty} \frac{1}{N}\#\left\{1\leq m\neq n \leq N : |x_m-x_n| \leq \frac{s}{N}\right\} = 2s.…

In this paper, we analyze the cross-correlation properties for Chu sequences, which provide information on the distribution of the maximum magnitudes of the cross-correlation function. Furthermore, we can obtain the number of available…

Let $p$ be an odd prime such that $p \equiv 3\;{\rm mod}\;4$ and $n$ be an odd integer. In this paper, two new families of $p$-ary sequences of period $N = \frac{p^n-1}{2}$ are constructed by two decimated $p$-ary m-sequences $m(2t)$ and…

We obtain the triple correlations for a truncated divisor sum related to primes. We also obtain the mixed correlations for this divisor sum when it is summed over the primes, and give some applications to primes in short intervals.

In a quantum dot with three leads the transmission matrix t_{12} between two of these leads is a truncation of a unitary scattering matrix S, which we treat as random. As the number of channels in the third lead is increased, the…