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arXiv · 1008.1615

Optimal Partitioned Cyclic Difference Packings for Frequency Hopping and Code Synchronization

Yeow Meng Chee·Alan C. H. Ling·Jianxing Yin
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Abstract

Optimal partitioned cyclic difference packings (PCDPs) are shown to give rise to optimal frequency-hopping sequences and optimal comma-free codes. New constructions for PCDPs, based on almost difference sets and cyclic difference matrices, are given. These produce new infinite families of optimal PCDPs (and hence optimal frequency-hopping sequences and optimal comma-free codes). The existence problem for optimal PCDPs in ${\mathbb Z}_{3m}$, with $m$ base blocks of size three, is also solved for all $m\not\equiv 8,16\pmod{24}$.

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Yeow Meng Chee, Alan C. H. Ling, Jianxing Yin. 2010-08-10. Optimal Partitioned Cyclic Difference Packings for Frequency Hopping and Code Synchronization. https://doi.org/10.1109/tit.2010.2070530

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