Complex periodic sequences with perfect out-of-phase autocorrelation coefficients

Abstract

In this thesis, we study complex periodic sequences where the entries are p-th roots of unity for an odd prime p. In addition, the sequences are required to have a perfect or nearly perfect out-of-phase autocorrelation coefficients. Such sequences are equivalent to certain relative difference sets and direct product difference sets, respectively. We obtain some new results on the necessary conditions for the existence of non-binary sequences. We also prove the nonexistence of (2p^s, p, 2p^s, 2p^{sa??1})- relative difference sets in any abelian group of order 2p^{s+1} and some results on the character values.