Optimal Partitioned Cyclic Difference Packings for Frequency Hopping and Code Synchronization
arXiv:1008.1615 · doi:10.1109/TIT.2010.2070530
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 $m\not\equiv 8,16\pmod{24}$.
to appear in IEEE Transactions on Information Theory