AMC
New constructions of optimal frequency hopping sequences with new parameters
Fang Liu Daiyuan Peng Zhengchun Zhou Xiaohu Tang
Advances in Mathematics of Communications 2013, 7(1): 91-101 doi: 10.3934/amc.2013.7.91
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.
keywords: Lempel-Greenberger bound. Generalized cyclotomy Hamming autocorrelation frequency-hopping sequences
AMC
New nearly optimal codebooks from relative difference sets
Zhengchun Zhou Xiaohu Tang
Advances in Mathematics of Communications 2011, 5(3): 521-527 doi: 10.3934/amc.2011.5.521
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 di erence sets. almost difference sets signal sets
AMC
Even periodic and odd periodic complementary sequence pairs from generalized Boolean functions
Yang Yang Xiaohu Tang Guang Gong
Advances in Mathematics of Communications 2013, 7(2): 113-125 doi: 10.3934/amc.2013.7.113
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.
keywords: Even periodic complementary sequence pair Golay complementary pair odd periodic complementary sequence pair Golay sequences generalized Boolean function.
AMC
New almost perfect, odd perfect, and perfect sequences from difference balanced functions with d-form property
Yang Yang Xiaohu Tang Guang Gong
Advances in Mathematics of Communications 2017, 11(1): 67-76 doi: 10.3934/amc.2017002

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.

keywords: Almost perfect sequences perfect sequences odd perfect sequences QAM+ sequences difference balanced function d-form.

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