A Kind of Disjoint Cyclic Perfect Mendelsohn Difference Family and Its Applications in Strictly Optimal FHSs

Special Section on Signal Design and Its Applications in Communications

Key Laboratory of Mathematics and Interdisciplinary Sciences, Guangdong Higher Education Institutes, Guangzhou University">Shanding XU, Xiwang CAO, Jian GAO, Chunming TANG

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Keywords: frequency-hopping sequence, strictly optimal, disjoint cyclic perfect Mendelsohn difference family, Zeng-Cai-Tang-Yang cyclotomy

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2018 Volume E101.A Issue 12 Pages 2338-2343

DOI https://doi.org/10.1587/transfun.E101.A.2338

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Abstract

As an optimal combinatorial object, cyclic perfect Mendelsohn difference family (CPMDF) was introduced by Fuji-Hara and Miao to construct optimal optical orthogonal codes. In this paper, we propose a direct construction of disjoint CPMDFs from the Zeng-Cai-Tang-Yang cyclotomy. Compared with a recent work of Fan, Cai, and Tang, our construction doesn't need to depend on a cyclic difference matrix. Furthermore, strictly optimal frequency-hopping sequences (FHSs) are a kind of optimal FHSs which has optimal Hamming auto-correlation for any correlation window. As an application of our disjoint CPMDFs, we present more flexible combinatorial constructions of strictly optimal FHSs, which interpret the previous construction proposed by Cai, Zhou, Yang, and Tang.

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