Partial direct product difference sets and sequences with ideal autocorrelation

Abstract

In this paper, we study the sequences with (non-consecutive) two zero-symbols and ideal autocorrelation, which are also known as almost m-ary nearly perfect sequences. We show that these sequences are equivalent to ℓ-partial direct product difference sets (PDPDS), then we extend known results on the sequences with two consecutive zero-symbols to nonconsecutive case. Next, we study the notion of multipliers and orbit combination for ℓ-PDPDS. Finally, we present a construction method for a family of almost quaternary sequences with ideal autocorrelation by using cyclotomic classes.