New sets of low-hit-zone frequency-hopping sequence with optimal maximum periodic partial Hamming correlation

Recently, Chung et al. gave a general method to construct frequency-hopping sequence set (FHS set) with low-hit-zone (LHZ FHS set) by the Cartesian product. In their paper, Theorems 5 and 8 claim that k FHS sets whose maximum periodic Hamming correlation is 0 at the origin result in an LHZ FHS set b...

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Bibliographic Details
Published in:Science China. Information sciences 2015-12, Vol.58 (12), p.1-15
Main Authors: Wang, ChangYuan, Peng, DaiYuan, Han, HongYu, Zhou, LiMengNan
Format: Article
Language:English
Subjects:
Cartesian
Cartesian coordinates
China
Computer Science
Construction
Correlation
Frequency hopping
Information Systems and Communication Service
Optimization
Origins
Research Paper
Upper bounds
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Summary:Recently, Chung et al. gave a general method to construct frequency-hopping sequence set (FHS set) with low-hit-zone (LHZ FHS set) by the Cartesian product. In their paper, Theorems 5 and 8 claim that k FHS sets whose maximum periodic Hamming correlation is 0 at the origin result in an LHZ FHS set based on the Cartesian product, and Proposition 4 presented an upper bound of the maximum periodic Hamming correlation of FHSs. However, their statements are imperfect or incorrect. In this paper, we give counterexamples and make corrections to them. Furthermore, based on the Cartesian product, we construct two classes of LHZ FHS sets with optimal maximum periodic partial Hamming correlation property. It is shown that new FHS sets are optimal by the maximum periodic partial Hamming correlation bound of LHZ FHS set.
ISSN:1674-733X
1869-1919
DOI:10.1007/s11432-015-5326-6