An Upper Bound of the Set Size of Perfect Sequences with Optimal Cross-correlation

The set of perfect sequences with optimal cross-correlation has applications in communication and radar systems. Many different constructions, which are called optimal sets of perfect sequences according to Sarwate bound, have been studied in the literature. However, Song et al. and Zhang et al. recently showed that the set size of these constructions can be improved, since the term related to size vanishes for perfect sequences in Sarwate bound. Until now, we don’t know whether the set size of these constructions is optimal, though they are all called optimal sets. We studied the problem of the set size of perfect sequences with optimal cross-correlation, and showed that the set size must be upper bounded by the length of the perfect sequences in this paper.