Optimal Partitioned Cyclic Difference Packings for Frequency Hopping and Code Synchronization

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 $m\not\equiv 8,16(\mathrm{mod}24)$.

to appear in IEEE Transactions on Information Theory

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