Related papers: Arithmetic crosscorrelation of binary $m$-sequence…

Let $p_{r+1}-1>n \geq p_r-1$, based on a sequence $\{1,2,3\cdots\ M_r(M_r=p_1p_2\cdots p_r)\}$, we compare the density of coprime numbers and establish a correlation between the proportions of coprime numbers in the ranges from 1 to…

New generalized cyclotomic binary sequences of period $p^2$ are proposed in this paper, where $p$ is an odd prime. The sequences are almost balanced and their linear complexity is determined. The result shows that the proposed sequences…

For a prime $p\ge 5$ let $q_0,q_1,\ldots,q_{(p-3)/2}$ be the quadratic residues modulo $p$ in increasing order. We study two $(p-3)/2$-periodic binary sequences $(d_n)$ and $(t_n)$ defined by $d_n=q_n+q_{n+1}\bmod 2$ and $t_n=1$ if…

Let $p$ be an odd prime with $2$-adic expansion $\sum_{i=0}^kp_i\cdot2^i$. For a sequence $\underline{a}=(a(t))_{t\ge 0}$ over $\mathbb{F}_{p}$, each $a(t)$ belongs to $\{0,1,\ldots, p-1\}$ and has a unique $2$-adic expansion…

We show that it is possible to algorithmically verify if a given pattern sequence is noncorrelated. As an application, we compute that there are exactly $2272$ noncorrelated binary pattern sequences of length $\leq 4$. If we restrict our…

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…

Binary cyclic codes are worth studying due to their applications and theoretical importance. It is an important problem to construct an infinite family of cyclic codes with large minimum distance $d$ and dual distance $d^{\perp}$. In recent…

It has been long conjectured that the crossing numbers of the complete bipartite graph K_{m,n} and of the complete graph K_n equal Z(m,n) (the value conjectured by Zarankiewicz, who came up with a drawing reaching this value) and Z(n)…

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…

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…

Optimal two-treatment, $p$ period crossover designs for binary responses are determined. The optimal designs are obtained by minimizing the variance of the treatment contrast estimator over all possible allocations of $n$ subjects to $2^p$…

For any $m = 3 \left( 2n + 1 \right) with \ n \in \mathbb{N^*} ,$ the prime counting function $\pi(m) = 4 + \left \vert A_4(m) \right \vert + 2 \left \vert A_6(m) \right \vert $ where $A_6(m) $ and $ A_4(m) $ are the sets of Twin Primes and…

In this paper, we make some progress towards a well-known conjecture on the minimum weights of binary cyclic codes with two primitive nonzeros. We also determine the Walsh spectrum of $\Tr(x^d)$ over $\F_{2^{m}}$ in the case where $m=2t$,…

We determine the minimum sum--connectivity index of bicyclic graphs with $n$ vertices and matching number $m$, where $2\le m\le \lfloor\frac{n}{2}\rfloor$, the minimum and the second minimum, as well as the maximum and the second maximum…

For any positive integer $m$, the complete graph on $2^{2m}(2^m+2)$ vertices is decomposed into $2^m+1$ commuting strongly regular graphs, which give rise to a symmetric association scheme of class $2^{m+2}-2$. Furthermore, the…

Through the following, we establish the conditions which allow us to express recursive sequences of real numbers, enumerated through the recurrence relation a_{n+1} = Aa_n + Ba_{n-1}, by means of algebraic equations in two variables of…

In this paper, a new method is presented to compute the 2-adic complexity of pseudo-random sequences. With this method, the 2-adic complexities of all the known sequences with ideal 2-level autocorrelation are uniformly determined. Results…

Binary sequences with lower autocorrelation values have important applications in cryptography and communications. In this paper, we present all possible parameters for binary periodical sequences with a 2-level autocorrelation values. For…

Correlation measure of order $k$ is an important measure of randomness in binary sequences. This measure tries to look for dependence between several shifted version of a sequence. We study the relation between the correlation measure of…

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…