More cyclotomic constructions of optimal frequency-hopping sequences

Shanding Xu; Xiwang Cao; Jiafu Mi; Chunming Tang

doi:10.3934/amc.2019024

Article Contents

2019, Volume 13, Issue 3: 373-391. Doi: 10.3934/amc.2019024

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$ {{\rm{PG}}}(4,q) $

More cyclotomic constructions of optimal frequency-hopping sequences

1.
Department of Mathematics and physics, Nanjing Institute of Technology, Nanjing 211167, China
2.
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
3.
Key Laboratory of Mathematics and Interdisciplinary Sciences, Guangdong Higher Education Institutes, Guangzhou University, Guangzhou 510006, China
4.
State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China

Received: April 30, 2017

Published: August 2019

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Abstract

In this paper, some general properties of the Zeng-Cai-Tang-Yang cyclotomy are studied. As its applications, two constructions of frequency-hopping sequences (FHSs) and two constructions of FHS sets are presented, where the length of sequences can be any odd integer larger than 3. The FHSs and FHS sets generated by our construction are (near-) optimal with respect to the Lempel–Greenberger bound and Peng–Fan bound, respectively. By choosing appropriate indexes and index sets, a lot of (near-) optimal FHSs and FHS sets can be obtained by our construction. Furthermore, some of them have new parameters which are not covered in the literature.

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Mathematics Subject Classification: 94A05, 94A55.

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