## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

AMC

In this paper, three constructions of frequency hopping sequences
(FHSs) are proposed using a new generalized cyclotomy with respect
to $\textbf{Z}_{p^n}$, where $p$ is an odd prime and $n$ is a
positive integer. Based on some basic properties of the new
generalized cyclotomy, it is shown that all the constructed FHSs are
optimal with respect to the well-known Lempel-Greenberger bound.
Furthermore, these FHSs have new parameters which are not reported
in the literature.

AMC

Codebooks achieving the Welch bound on the maximum correlation
amplitude are desirable in a number of applications. Recently,
codebooks meeting (resp., nearly meeting) the Welch bound were
constructed from difference sets (resp., almost difference sets). In
this paper, a general connection between complex codebooks and
relative difference sets is introduced. Several classes of codebooks
nearly meeting the Welch bound are then constructed from some known
relative difference sets using the general connection.

keywords:
Welch bound
,
Codebooks
,
difference sets
,
relative dierence sets.
,
almost difference sets
,
signal sets

AMC

A pair of two sequences is called the even periodic (odd periodic)
complementary sequence pair if the sum of their even periodic (odd
periodic) correlation function is a delta function. The well-known
Golay aperiodic complementary sequence pair (Golay pair) is a
special case of even periodic (odd periodic) complementary sequence
pair. In this paper, we presented several classes of even periodic
and odd periodic complementary pairs based on the generalized
Boolean functions, but which do not form Gloay pairs. The proposed
sequences could be used to design signal sets, which have been
applied in direct sequence code division multiple (DS-CDMA) cellular
communication systems.

AMC

By using shift sequences defined by difference balanced functions with *d*-form property, and column sequences defined by a mutually orthogonal almost perfect sequences pair, new almost perfect, odd perfect, and perfect sequences are obtained via interleaving method. Furthermore, the proposed perfect QAM+ sequences positively answer to the problem of the existence of perfect QAM+ sequences proposed by Boztaş and Udaya.

AMC

A sequence is called perfect if its autocorrelation function is a
delta function. In this paper, we give a new definition of
autocorrelation function: $\omega$-cyclic-conjugated autocorrelation. As a result, we present several classes of $\omega$-cyclic-conjugated-perfect quaternary Golay sequences, where $\omega=\pm 1$. We also considered
such perfect property for $4^q$-QAM Golay sequences, $q\ge 2$ being an integer.

AMC

A class of quaternary sequences $\mathbb{S}_{\lambda}$ had been proven to be optimal for some special values of $\lambda$. In this note, $\mathbb{S}_{\lambda}$ is investigated for all $\lambda$ by virtue of the $\mathbb{Z}_4$-valued quadratic forms over Galois rings. As a consequence, a new class of quaternary sequences with low correlation is obtained and the correlation distribution is also completely determined. It also turns out that the known optimal quaternary sequences $\mathbb{S}_{\lambda}$ for particular $\lambda$ can be easily obtained from our approach.

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