New constructions of optimal frequency hopping sequences with new parameters

Fang Liu; Daiyuan Peng; Zhengchun Zhou; Xiaohu Tang

doi:10.3934/amc.2013.7.91

Article Contents

2013, Volume 7, Issue 1: 91-101. Doi: 10.3934/amc.2013.7.91

This issue Previous Article Self-dual $\mathbb{F}_q$-linear $\mathbb{F}_{q^t}$-codes with an automorphism of prime order Next Article Generalizations of Verheul's theorem to asymmetric pairings

New constructions of optimal frequency hopping sequences with new parameters

1.
The Thirtieth Research Institute, China Electronic Technology Group Corporation, Chengdu
2.
School of Mobile Communications, Southwest Jiaotong University, Chengdu, 610031
3.
School of Mathematics, Southwest Jiaotong University, Chengdu, 610031

Received: May 31, 2012

Published: January 2013

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Abstract

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.

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Mathematics Subject Classification: Primary: 94A05, 94B60; Secondary: 05B10.

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